qu.env.lastSaved= Aug 11, 2005 10:51:59 PM @ qu.env.validTest= true @ qu.1.topic=9_1 Square Roots@ qu.1.1.mode=Multi Formula@ qu.1.1.name=int lt 10 +@ qu.1.1.comment=
Find 
$num
 

$num
 = 
$ans • $ans
 = $ans
@ qu.1.1.editing=useHTML@ qu.1.1.algorithm=$ans=range(2,10,1); $num=$ans^2;@ qu.1.1.question=
Find 
$num
 
When multiple answers exist, enter each value separated by a semi-colon as 3; -3.@ qu.1.1.answer=$ans@ qu.1.2.mode=Multi Formula@ qu.1.2.name=int lt 10 -@ qu.1.2.comment=
Find    −
$num
 
When multiple answers exist, enter each value separated by a semi-colon as 3; -3.
−
$num
 = −
$ans • $ans
 = ${-1*$ans}
@ qu.1.2.editing=useHTML@ qu.1.2.algorithm=$ans=range(2,10,1); $num=$ans^2;@ qu.1.2.question=
Find    −
$num
 
When multiple answers exist, enter each value separated by a semi-colon as 3; -3.@ qu.1.2.answer=${-1*$ans}@ qu.1.3.mode=Multi Formula@ qu.1.3.name=int gt 10 +@ qu.1.3.comment=
Find 
$num
 

$num
 = 
$ans • $ans
 = $ans
@ qu.1.3.editing=useHTML@ qu.1.3.algorithm=$ans=range(11,25,1); $num=$ans^2;@ qu.1.3.question=
Find 
$num
 
When multiple answers exist, enter each value separated by a semi-colon as 3; -3.@ qu.1.3.answer=$ans@ qu.1.4.mode=Multi Formula@ qu.1.4.name=int gt 10 -@ qu.1.4.comment=
Find    −
$num
 
When multiple answers exist, enter each value separated by a semi-colon as 3; -3.
−
$num
 = −
$ans • $ans
 = ${-1*$ans}
@ qu.1.4.editing=useHTML@ qu.1.4.algorithm=$ans=range(11,25,1); $num=$ans^2;@ qu.1.4.question=
Find    −
$num
 
When multiple answers exist, enter each value separated by a semi-colon as 3; -3.@ qu.1.4.answer=${-1*$ans}@ qu.2.topic=9_1 Approximate Square Roots@ qu.2.1.mode=Multi Formula@ qu.2.1.name=int lt 10 +@ qu.2.1.comment=
Find 
$num
 

$num
 = $ans
Round to the nearest tenth.
$ans2 @ qu.2.1.editing=useHTML@ qu.2.1.algorithm=$num=range(10,100,1); $ans=sqrt($num); condition:ne(int($ans),$ans); $ans2=decimal(1,$ans);@ qu.2.1.question=
Find 
$num
 
Round answers to the nearest tenth.
When multiple answers exist, enter each value separated by a semi-colon as 3; -3.@ qu.2.1.answer=$ans2@ qu.2.2.mode=Multi Formula@ qu.2.2.name=int lt 10 -@ qu.2.2.comment=
Find    −
$num
 
Round answers to the nearest tenth.
When multiple answers exist, enter each value separated by a semi-colon as 3; -3.
−
$num
 = ${-1*$ans}
Round to the nearest tenth.
${-1*$ans2} @ qu.2.2.editing=useHTML@ qu.2.2.algorithm=$num=range(10,100,1); $ans=sqrt($num); condition:ne(int($ans),$ans); $ans2=decimal(1,$ans);@ qu.2.2.question=
Find    −
$num
 
Round answers to the nearest tenth.
When multiple answers exist, enter each value separated by a semi-colon as 3; -3.@ qu.2.2.answer=${-1*$ans2}@ qu.2.3.mode=Multi Formula@ qu.2.3.name=int gt 10 +@ qu.2.3.comment=
Find 
$num
 

$num
 = $ans
Round to the nearest tenth.
$ans2 @ qu.2.3.editing=useHTML@ qu.2.3.algorithm=$num=range(100,624,1); $ans=sqrt($num); condition:ne(int($ans),$ans); $ans2=decimal(1,$ans);@ qu.2.3.question=
Find 
$num
 
Round answers to the nearest tenth.
When multiple answers exist, enter each value separated by a semi-colon as 3; -3.@ qu.2.3.answer=$ans2@ qu.2.4.mode=Multi Formula@ qu.2.4.name=int gt 10 -@ qu.2.4.comment=
Find    −
$num
 
Round answers to the nearest tenth.
When multiple answers exist, enter each value separated by a semi-colon as 3; -3.
−
$num
 = ${-1*$ans}
Round to the nearest tenth.
${-1*$ans2} @ qu.2.4.editing=useHTML@ qu.2.4.algorithm=$num=range(100,624,1); $ans=sqrt($num); condition:ne(int($ans),$ans); $ans2=decimal(1,$ans);@ qu.2.4.question=
Find    −
$num
 
Round answers to the nearest tenth.
When multiple answers exist, enter each value separated by a semi-colon as 3; -3.@ qu.2.4.answer=${-1*$ans2}@ qu.3.topic=9_1 Solve Using Square Roots A@ qu.3.1.mode=Multi Formula@ qu.3.1.name=x^2 = a@ qu.3.1.comment=

Solve the equation.
$x2 = $a

Take the square root of both sides.

x = ±
$a
 
x = ± $ans
Enter the answers as $ans; ${-1*$ans} @ qu.3.1.editing=useHTML@ qu.3.1.algorithm=$ans=range(5,25,1); $a=$ans^2; $x=switch(rint(4),"w","x","y","z");@ qu.3.1.question=

Solve the equation.
$x2 = $a
When multiple answers exist, enter each value separated by a semi-colon as 3; -3.

@ qu.3.1.answer=$ans; ${-1*$ans}@ qu.3.2.mode=Multi Formula@ qu.3.2.name=y^2 = a@ qu.3.2.comment=

Solve the equation.
$x2 = $a

Take the square root of both sides.

x = ±
$a
 
x = ± $ans
Enter the answers as $ans; ${-1*$ans} @ qu.3.2.editing=useHTML@ qu.3.2.algorithm=$ans=range(5,25,1); $a=$ans^2; $x=switch(rint(4),"w","x","y","z");@ qu.3.2.question=

Solve the equation.
$x2 = $a
When multiple answers exist, enter each value separated by a semi-colon as 3; -3.

@ qu.3.2.answer=$ans; ${-1*$ans}@ qu.4.topic=9_1 Solve Using Square Roots B@ qu.4.1.mode=Multi Formula@ qu.4.1.name=x^2 - a = b@ qu.4.1.comment=

Solve the equation.
$x2 - $a = $b
When multiple answers exist, enter each value separated by a semi-colon as 3; -3.

Add $a to both sides.
$x2 = ${$a+$b}
Take the square root of both sides.

x = ±
${$a+$b}
 
x = ± $ans
Enter the answers as $ans; ${-1*$ans}@ qu.4.1.editing=useHTML@ qu.4.1.algorithm=$ans=range(6,12,1); $a=range(15,$ans^2-10); $b=$ans^2-$a; condition:gt($b,0);@ qu.4.1.question=Solve the equation.
$x2 - $a = $b
When multiple answers exist, enter each value separated by a semi-colon as 3; -3.
Round to the nearest tenth when necessary.@ qu.4.1.answer=$ans; ${-1*$ans}@ qu.4.2.mode=Multi Formula@ qu.4.2.name=x^2 - a = 0@ qu.4.2.comment=

Solve the equation.
$x2 - $a = $b
When multiple answers exist, enter each value separated by a semi-colon as 3; -3.

Add $a to both sides.
$x2 = ${$a+$b}
Take the square root of both sides.

x = ±
${$a+$b}
 
x = ± $ans
Enter the answers as $ans; ${-1*$ans}@ qu.4.2.editing=useHTML@ qu.4.2.algorithm=$ans=range(6,12,1); $a=$ans^2; $b=0;@ qu.4.2.question=Solve the equation.
$x2 - $a = $b
When multiple answers exist, enter each value separated by a semi-colon as 3; -3.
Round to the nearest tenth when necessary.@ qu.4.2.answer=$ans; ${-1*$ans}@ qu.4.3.mode=Multi Formula@ qu.4.3.name=x^2 + a = b@ qu.4.3.comment=

Solve the equation.
$x2 + $a = $b
When multiple answers exist, enter each value separated by a semi-colon as 3; -3.

Subtract $a from both sides.
$x2 = ${$b-$a}
Take the square root of both sides.

x = ±
${$b-$a}
 
x = ± $ans
Enter the answers as $ans; ${-1*$ans} @ qu.4.3.editing=useHTML@ qu.4.3.algorithm=$ans=range(6,12,1); $a=range(15,$ans^2-10); $b=$ans^2+$a; condition:gt($b,0);@ qu.4.3.question=Solve the equation.
$x2 + $a = $b
When multiple answers exist, enter each value separated by a semi-colon as 3; -3.
Round to the nearest tenth when necessary.@ qu.4.3.answer=$ans; ${-1*$ans}@ qu.5.topic=9_1 Solve Using Square Roots C@ qu.5.1.mode=Multi Formula@ qu.5.1.name=x^2 - a = b@ qu.5.1.comment=

Solve the equation.
$x2 - $a = $b
When multiple answers exist, enter each value separated by a semi-colon as 3; -3.

Add $a to both sides.
$x2 = ${$a+$b}
Take the square root of both sides.

x = ±
${$a+$b}
 
x = ± $ans
Enter the answers as $ans; ${-1*$ans}@ qu.5.1.editing=useHTML@ qu.5.1.algorithm=$num=range(20,250,1); $a=range(9,$num-10); $b=$num-$a; condition:gt($b,0); $ans=decimal(1,sqrt($num)); condition:ne($ans,int($ans));@ qu.5.1.question=Solve the equation.
$x2 - $a = $b
When multiple answers exist, enter each value separated by a semi-colon as 3; -3.
Round to the nearest tenth when necessary.@ qu.5.1.answer=$ans; ${-1*$ans}@ qu.5.2.mode=Multi Formula@ qu.5.2.name=x^2 - a = 0@ qu.5.2.comment=

Solve the equation.
$x2 - $a = $b
When multiple answers exist, enter each value separated by a semi-colon as 3; -3.

Add $a to both sides.
$x2 = ${$a+$b}
Take the square root of both sides.

x = ±
${$a+$b}
 
x = ± $ans
Enter the answers as $ans; ${-1*$ans}@ qu.5.2.editing=useHTML@ qu.5.2.algorithm=$num=range(20,250,1); $a=$num; $b=0; $ans=decimal(1,sqrt($num)); condition:ne($ans,int($ans));@ qu.5.2.question=Solve the equation.
$x2 - $a = $b
When multiple answers exist, enter each value separated by a semi-colon as 3; -3.
Round to the nearest tenth when necessary.@ qu.5.2.answer=$ans; ${-1*$ans}@ qu.5.3.mode=Multi Formula@ qu.5.3.name=x^2 + a = b@ qu.5.3.comment=

Solve the equation.
$x2 + $a = $b
When multiple answers exist, enter each value separated by a semi-colon as 3; -3.

Subtract $a from both sides.
$x2 = ${$b-$a}
Take the square root of both sides.

x = ±
${$b-$a}
 
x = ± $ans
Enter the answers as $ans; ${-1*$ans} @ qu.5.3.editing=useHTML@ qu.5.3.algorithm=$num=range(20,250,1); $a=range(9,$num-10); $b=$num+$a; condition:gt($b,0); $ans=decimal(1,sqrt($num)); condition:ne($ans,int($ans));@ qu.5.3.question=Solve the equation.
$x2 + $a = $b
When multiple answers exist, enter each value separated by a semi-colon as 3; -3.
Round to the nearest tenth when necessary.@ qu.5.3.answer=$ans; ${-1*$ans}@ qu.6.topic=9_2 Classify Real Numbers@ qu.6.1.mode=Multiple Selection@ qu.6.1.name=A@ qu.6.1.comment=
$rt
 is a rational number because $rt is a perfect square. The square root of $rt is ${sqrt($rt)};
0.${$a}${$b}${$a}${$a}${$b}${$a}${$a}${$a}${$b}....  is an irrational number since the decimal does not repeat the same pattern each time.
$nrt
 is an irrational number since the square root of $nrt is not a perfect square and the decimal ${sqrt($nrt)} does not terminate or repeat.
${$d1}.${$n1}${$n1}${$d1}${$n1}${$n1}${$d1}${$n1}${$n1}${$d1}....  is a rational number since the decimal does repeat the same pattern ${$n1}${$n1}${$d1} each time.
@ qu.6.1.editing=useHTML@ qu.6.1.algorithm=$i=rint(3); $d1=range(1,9,1); $n1=range(1,9,1); condition:ne($n1,$d1); $rt=range(3,8,1)^2; $rt2=range(3,8,1)^2; $nrt=range(26,48); $nrt2=range(26,48); condition:ne($nrt,36); condition:ne($nrt2,36); $d2=switch($i,4,5,8); $n2=range(1,$d2-1,1); $a=range(1,9,2); $b=range(2,8,2); $td=$n2/$d2; $nt=range(25,100,1);@ qu.6.1.question=Check each box beside a value which is rational.@ qu.6.1.answer=1, 4@ qu.6.1.choice.1=
$rt
@ qu.6.1.choice.2=0.${$a}${$b}${$a}${$a}${$b}${$a}${$a}${$a}${$b}....@ qu.6.1.choice.3=
$nrt
@ qu.6.1.choice.4=${$d1}.${$n1}${$n1}${$d1}${$n1}${$n1}${$d1}${$n1}${$n1}${$d1}....@ qu.6.2.mode=Multiple Selection@ qu.6.2.name=B@ qu.6.2.comment=
$rt
 is a rational number because $rt is a perfect square. The square root of $rt is ${sqrt($rt)};
0.${$a}${$b}${$a}${$a}${$b}${$a}${$a}${$a}${$b}....  is an irrational number since the decimal does not repeat the same pattern each time.
$nrt
 is an irrational number since the square root of $nrt is not a perfect square and the decimal ${sqrt($nrt)} does not terminate or repeat.
${$d1}.${$n1}${$n1}${$d1}${$n1}${$n1}${$d1}${$n1}${$n1}${$d1}....  is a rational number since the decimal does repeat the same pattern ${$n1}${$n1}${$d1} each time.
@ qu.6.2.editing=useHTML@ qu.6.2.algorithm=$i=rint(3); $d1=range(1,9,1); $n1=range(1,9,1); condition:ne($n1,$d1); $rt=range(3,8,1)^2; $rt2=range(3,8,1)^2; $nrt=range(26,48); $nrt2=range(26,48); condition:ne($nrt,36); condition:ne($nrt2,36); $d2=switch($i,4,5,8); $n2=range(1,$d2-1,1); $a=range(1,9,2); $b=range(2,8,2); $td=$n2/$d2; $nt=range(25,100,1);@ qu.6.2.question=Check each box beside a value which is irrational.@ qu.6.2.answer=2, 3@ qu.6.2.choice.1=
$rt
@ qu.6.2.choice.2=0.${$a}${$b}${$a}${$a}${$b}${$a}${$a}${$a}${$b}....@ qu.6.2.choice.3=
$nrt
@ qu.6.2.choice.4=${$d1}.${$n1}${$n1}${$d1}${$n1}${$n1}${$d1}${$n1}${$n1}${$d1}....@ qu.6.3.mode=Multiple Selection@ qu.6.3.name=C@ qu.6.3.comment=
$rt
 is a rational number because $rt is a perfect square. The square root of $rt is ${sqrt($rt)};
$n1
$d1
 is a rational number since it can be written as a fraction.
$nrt
 is an irrational number since the square root of $nrt is not a perfect square and the decimal ${sqrt($nrt)} does not terminate or repeat.
${$d1}.${$n1}${$n1}${$d1}${$n1}${$n1}${$d1}${$n1}${$n1}${$d1}....  is a rational number since the decimal does repeat the same pattern ${$n1}${$n1}${$d1} each time.

@ qu.6.3.editing=useHTML@ qu.6.3.algorithm=$i=rint(3); $d1=range(1,9,1); $n1=range(1,9,1); condition:ne($n1,$d1); $rt=range(3,8,1)^2; $rt2=range(3,8,1)^2; $nrt=range(26,48); $nrt2=range(26,48); condition:ne($nrt,36); condition:ne($nrt2,36); $d2=switch($i,4,5,8); $n2=range(1,$d2-1,1); $a=range(1,9,2); $b=range(2,8,2); $td=$n2/$d2; $nt=range(25,100,1);@ qu.6.3.question=Check each box beside a value which is irrational.@ qu.6.3.answer=3@ qu.6.3.choice.1=
$rt
@ qu.6.3.choice.2=
$n1
$d1
@ qu.6.3.choice.3=
$nrt
@ qu.6.3.choice.4=${$d1}.${$n1}${$n1}${$d1}${$n1}${$n1}${$d1}${$n1}${$n1}${$d1}....@ qu.6.4.mode=Multiple Selection@ qu.6.4.name=D@ qu.6.4.comment=
$rt
 is a rational number because $rt is a perfect square. The square root of $rt is ${sqrt($rt)};
$n1
$d1
 is a rational number since it can be written as a fraction.
$nrt
 is an irrational number since the square root of $nrt is not a perfect square and the decimal ${sqrt($nrt)} does not terminate or repeat.
${$d1}.${$n1}${$n1}${$d1}${$n1}${$n1}${$d1}${$n1}${$n1}${$d1}....  is a rational number since the decimal does repeat the same pattern ${$n1}${$n1}${$d1} each time.

@ qu.6.4.editing=useHTML@ qu.6.4.algorithm=$i=rint(3); $d1=range(1,9,1); $n1=range(1,9,1); condition:ne($n1,$d1); $rt=range(3,8,1)^2; $rt2=range(3,8,1)^2; $nrt=range(26,48); $nrt2=range(26,48); condition:ne($nrt,36); condition:ne($nrt2,36); $d2=switch($i,4,5,8); $n2=range(1,$d2-1,1); $a=range(1,9,2); $b=range(2,8,2); $td=$n2/$d2; $nt=range(25,100,1);@ qu.6.4.question=Check each box beside a value which is rational.@ qu.6.4.answer=1, 2, 4@ qu.6.4.choice.1=
$rt
@ qu.6.4.choice.2=
$n1
$d1
@ qu.6.4.choice.3=
$nrt
@ qu.6.4.choice.4=${$d1}.${$n1}${$n1}${$d1}${$n1}${$n1}${$d1}${$n1}${$n1}${$d1}....@ qu.7.topic=9_2 Order Real Numbers A@ qu.7.1.mode=Blanks@ qu.7.1.name=Repeating Decimal lt@ qu.7.1.comment=Compare the values using <, > or =.
__
0. $r   and   $n2

The repeating decimal 0.${$r}${$r}${$r}${$r}... is less than $n2.@ qu.7.1.editing=useHTML@ qu.7.1.algorithm=$r1=range(2,9,1);$r2=range(2,9,1);condition:ne($r1,$r2);$r=$r1*10+$r2; $n1=$r/100; $n2=($r+1)/100;@ qu.7.1.question=Compare the values using <, >, or =.
__
0. $r <1> $n2
@ qu.7.1.blank.1=%3c@ qu.7.1.extra=%3e,%3d@ qu.7.2.mode=Blanks@ qu.7.2.name=Repeating Decimal gt@ qu.7.2.comment=Compare the values using <, > or =.
__
0. $r and $n2

The repeating decimal 0.${$r}${$r}${$r}${$r}... is greater than $n2.@ qu.7.2.editing=useHTML@ qu.7.2.algorithm=$r1=range(2,9,1);$r2=range(2,9,1);condition:ne($r1,$r2);$r=$r1*10+$r2; $n1=$r/100; $n2=($r)/100;@ qu.7.2.question=Compare the values using <, >, or =.
__
0. $r <1> $n2
@ qu.7.2.blank.1=%3e@ qu.7.2.extra=%3c,%3d@ qu.7.3.mode=Blanks@ qu.7.3.name=Repeating Decimal gt -@ qu.7.3.comment=Compare the values using <, > or =.
__
-0. $r and ${-1*$n2}

The repeating decimal -0.${$r}${$r}${$r}${$r}... is greater than ${-1*$n2}.@ qu.7.3.editing=useHTML@ qu.7.3.algorithm=$r1=range(2,9,1);$r2=range(2,9,1);condition:ne($r1,$r2);$r=$r1*10+$r2; $n1=$r/100; $n2=($r+1)/100;@ qu.7.3.question=Compare the values using <, >, or =.
__
-0. $r <1> ${-1*$n2}
@ qu.7.3.blank.1=%3e@ qu.7.3.extra=%3d,%3c@ qu.7.4.mode=Blanks@ qu.7.4.name=Repeating Decimal lt -@ qu.7.4.comment=Compare the values using <, > or =.
__
-0. $r and ${-1*$n2}

The repeating decimal -0.${$r}${$r}${$r}${$r}... is less than ${-1*$n2}.@ qu.7.4.editing=useHTML@ qu.7.4.algorithm=$r1=range(2,9,1);$r2=range(2,9,1);condition:ne($r1,$r2);$r=$r1*10+$r2; $n1=$r/100; $n2=($r)/100;@ qu.7.4.question=Compare the values using <, >, or =.
__
-0. $r <1> ${-1*$n2}
@ qu.7.4.blank.1=%3c@ qu.7.4.extra=%3d,%3e@ qu.7.5.mode=Blanks@ qu.7.5.name=repeating decimal =@ qu.7.5.comment=Compare the values 
  __
0. $r
 and  
$n
11
using <, > or =.

$n
11
  is 0.${$r}${$r}${$r} which is equal to 0.${$r}${$r}${$r}${$r}....
@ qu.7.5.editing=useHTML@ qu.7.5.algorithm=$n=range(2,9); $r=$n*9;@ qu.7.5.question= Compare the values using <, > or =.
__
0. $r
<1>
$n
11
@ qu.7.5.blank.1=%3d@ qu.7.5.extra=%3c,%3e@ qu.8.topic=9_2 Order Real Numbers B@ qu.8.1.mode=Blanks@ qu.8.1.name=root gt +@ qu.8.1.comment= Compare the values using <, > or =.
$n1
and $n2
$n1
 = ${sqrt($n1)} and is greater than $n2
@ qu.8.1.editing=useHTML@ qu.8.1.algorithm=$n2=range(5,15,1); $n1=$n2^2+range(1,10,1);@ qu.8.1.question= Compare the values using <, > or =.
$n1
<1> $n2
@ qu.8.1.blank.1=%3e@ qu.8.1.extra=%3c,%3d@ qu.8.2.mode=Blanks@ qu.8.2.name=root lt +@ qu.8.2.comment= Compare the values using <, > or =.
$n1
and $n2
$n1
 = ${sqrt($n1)} and is less than $n2
@ qu.8.2.editing=useHTML@ qu.8.2.algorithm=$n2=range(5,15,1); $n1=$n2^2-range(1,10,1);@ qu.8.2.question= Compare the values using <, > or =.
$n1
<1> $n2
@ qu.8.2.blank.1=%3c@ qu.8.2.extra=%3e,%3d@ qu.8.3.mode=Blanks@ qu.8.3.name=root lt -@ qu.8.3.comment=

Compare the values using <, >, or =.

-
$n1
and ${-1*$n2}
-
$n1
= ${-1*sqrt($n1)} and is less than ${-1*$n2}
@ qu.8.3.editing=useHTML@ qu.8.3.algorithm=$n2=range(5,15,1); $n1=$n2^2+range(1,10,1);@ qu.8.3.question= Compare the values using <, > or =.
-
$n1
<1> ${-1*$n2}
@ qu.8.3.blank.1=%3c@ qu.8.3.extra=%3e,%3d@ qu.8.4.mode=Blanks@ qu.8.4.name=root gt -@ qu.8.4.comment=

Compare the values using <, >, or =.

-
$n1
and ${-1*$n2}
-
$n1
= ${-1*sqrt($n1)} and is greater than ${-1*$n2}
@ qu.8.4.editing=useHTML@ qu.8.4.algorithm=$n2=range(5,15,1); $n1=$n2^2-range(1,10,1);@ qu.8.4.question= Compare the values using <, > or =.
-
$n1
<1> ${-1*$n2}
@ qu.8.4.blank.1=%3e@ qu.8.4.extra=%3c,%3d@ qu.9.topic=9_3 Find Leg of Rt. Triangle A@ qu.9.1.question=

Find the length of the missing leg of the right triangle.
Round answers to the nearest tenth when necessary.

a = ?, b = $b, c = $c

@ qu.9.1.answer.num=$a@ qu.9.1.answer.units=@ qu.9.1.showUnits=false@ qu.9.1.grading=exact_value@ qu.9.1.negStyle=minus@ qu.9.1.numStyle=thousands scientific dollars arithmetic@ qu.9.1.mode=Numeric@ qu.9.1.name=find a@ qu.9.1.comment=

Find the length of the missing leg of the right triangle.
Round answers to the nearest tenth when necessary.

a = ?, b = $b, c = $c

Pythagorean Theorem
a2 + b2 = c2
Substitute
a2 + $b2 = $c2
Evaluate powers
a2 + ${$b^2} = ${$c^2}
Solve for a 2
a2 = ${$c^2-$b^2}
Take the positive square root of both sides.

a =
${$c^2-$b^2}
 = $a
@ qu.9.1.editing=useHTML@ qu.9.1.algorithm=$i=rint(5); $a=switch($i,3,6,5,9,8); $b=switch($i,4,8,12,12,15); $c=sqrt($a^2+$b^2); condition:eq(int($c),$c);@ qu.9.2.question=

Find the length of the missing leg of the right triangle.
Round answers to the nearest tenth when necessary.

a = $a, b = ?, c = $c

@ qu.9.2.answer.num=$b@ qu.9.2.answer.units=@ qu.9.2.showUnits=false@ qu.9.2.grading=exact_value@ qu.9.2.negStyle=minus@ qu.9.2.numStyle=thousands scientific dollars arithmetic@ qu.9.2.mode=Numeric@ qu.9.2.name=find b@ qu.9.2.comment=

Find the length of the missing leg of the right triangle.
Round answers to the nearest tenth when necessary.

a = $a, b = ?, c = $c

Pythagorean Theorem
a2 + b2 = c2
Substitute
$a2 + b2 = $c2
Evaluate powers
${$a^2} + b2 = ${$c^2}
Solve for b2
b2 = ${$c^2-$a^2}
Take the positive square root of both sides.

b =
${$c^2-$a^2}
 = $b
@ qu.9.2.editing=useHTML@ qu.9.2.algorithm=$i=rint(5); $a=switch($i,3,6,5,9,8); $b=switch($i,4,8,12,12,15); $c=sqrt($a^2+$b^2); condition:eq(int($c),$c);@ qu.10.topic=9_3 Find Hyp. of Rt. Triangle A@ qu.10.1.question=

Find the length of the hypotenuse of the right triangle.
Round answers to the nearest tenth when necessary.

a = $a, b = $b, c = ?

@ qu.10.1.answer.num=$c@ qu.10.1.answer.units=@ qu.10.1.showUnits=false@ qu.10.1.grading=exact_value@ qu.10.1.negStyle=minus@ qu.10.1.numStyle=thousands scientific dollars arithmetic@ qu.10.1.mode=Numeric@ qu.10.1.name=find h@ qu.10.1.comment=

Find the length of the hypotenuse of the right triangle.
Round answers to the nearest tenth when necessary.

a = $a, b = $b, c = ?

Pythagorean Theorem
a2 + b2 = c2
Substitute
$a2 + $b2 = c2
Evaluate powers
${$a^2} + ${$b^2} = c2
Add
${$a^2+$b^2} = c2
Take the positive square root of both sides.

c =
${$a^2+$b^2}
 = $c
@ qu.10.1.editing=useHTML@ qu.10.1.algorithm=$i=rint(5); $a=switch($i,12,7,15,10,20); $b=switch($i,16,24,20,24,21); $c=sqrt($a^2+$b^2); condition:eq(int($c),$c);@ qu.11.topic=9_3 Determine Right Triangle@ qu.11.1.mode=Multiple Selection@ qu.11.1.name=1 correct@ qu.11.1.comment=

Place a check beside each set of sides of a triangle which form a right triangle.
For each triangle, use the pythagorean theorem to check if the triangle is a right triangle.
a2 + b2 = c2

a = $a, b = $b, c = $c
${$a^2} + ${$b^2} ? ${$c^2}
${$a^2+$b^2} ? ${$c^2}
The statement is true. The triangle is a right triangle.

a = $a1, b = $b1, c = $c1
${$a1^2} + ${$b1^2} ? ${$c1^2}
${$a1^2+$b1^2} ? ${$c1^2}
The statement is false. The triangle is not a right triangle.

a = $a2, b = $b2, c = $c2
${$a2^2} + ${$b2^2} ? ${$c2^2}
${$a2^2+$b2^2} ? ${$c2^2}
The statement is false. The triangle is not a right triangle.

@ qu.11.1.editing=useHTML@ qu.11.1.algorithm=$i=rint(5); $a=switch($i,18,16,21,12,15); $b=switch($i,24,30,28,35,36); $c=sqrt($a^2+$b^2); condition:eq(int($c),$c); $j=rint(5); $a1=switch($j,24,9,27,14,30); $b1=switch($j,32,40,36,48,40); $c1=sqrt($a1^2+$b1^2)-1; $k=rint(5); $a2=switch($k,24,20,28,33,40); $b2=switch($k,45,48,45,44,42); $c2=sqrt($a2^2+$b2^2)+1;@ qu.11.1.question=Place a check beside each set of sides of a triangle which form a right triangle.@ qu.11.1.answer=1@ qu.11.1.choice.1=a = $a, b = $b, c = $c@ qu.11.1.choice.2=a = $a1, b = $b1, c = $c1@ qu.11.1.choice.3=a = $a2, b = $b2, c = $c2@ qu.11.2.mode=Multiple Selection@ qu.11.2.name=2 correct@ qu.11.2.comment=

Place a check beside each set of sides of a triangle which form a right triangle.
For each triangle, use the pythagorean theorem to check if the triangle is a right triangle.
a2 + b2 = c2

a = $a, b = $b, c = $c
${$a^2} + ${$b^2} ? ${$c^2}
${$a^2+$b^2} ? ${$c^2}
The statement is true. The triangle is a right triangle.

a = $a1, b = $b1, c = $c1
${$a1^2} + ${$b1^2} ? ${$c1^2}
${$a1^2+$b1^2} ? ${$c1^2}
The statement is true. The triangle is a right triangle.

a = $a2, b = $b2, c = $c2
${$a2^2} + ${$b2^2} ? ${$c2^2}
${$a2^2+$b2^2} ? ${$c2^2}
The statement is false. The triangle is not a right triangle.

@ qu.11.2.editing=useHTML@ qu.11.2.algorithm=$i=rint(5); $a=switch($i,18,16,21,12,15); $b=switch($i,24,30,28,35,36); $c=sqrt($a^2+$b^2); condition:eq(int($c),$c); $j=rint(5); $a1=switch($j,24,9,27,14,30); $b1=switch($j,32,40,36,48,40); $c1=sqrt($a1^2+$b1^2); condition:eq(int($c1),$c1); $k=rint(5); $a2=switch($k,24,20,28,33,40); $b2=switch($k,45,48,45,44,42); $c2=sqrt($a2^2+$b2^2)+1;@ qu.11.2.question=Place a check beside each set of sides of a triangle which form a right triangle.@ qu.11.2.answer=1, 2@ qu.11.2.choice.1=a = $a, b = $b, c = $c@ qu.11.2.choice.2=a = $a1, b = $b1, c = $c1@ qu.11.2.choice.3=a = $a2, b = $b2, c = $c2@ qu.11.3.mode=Multiple Selection@ qu.11.3.name=3 correct@ qu.11.3.comment=

Place a check beside each set of sides of a triangle which form a right triangle.
For each triangle, use the pythagorean theorem to check if the triangle is a right triangle.
a2 + b2 = c2

a = $a, b = $b, c = $c
${$a^2} + ${$b^2} ? ${$c^2}
${$a^2+$b^2} ? ${$c^2}
The statement is true. The triangle is a right triangle.

a = $a1, b = $b1, c = $c1
${$a1^2} + ${$b1^2} ? ${$c1^2}
${$a1^2+$b1^2} ? ${$c1^2}
The statement is true. The triangle is a right triangle.

a = $a2, b = $b2, c = $c2
${$a2^2} + ${$b2^2} ? ${$c2^2}
${$a2^2+$b2^2} ? ${$c2^2}
The statement is true. The triangle is a right triangle.

@ qu.11.3.editing=useHTML@ qu.11.3.algorithm=$i=rint(5); $a=switch($i,18,16,21,12,15); $b=switch($i,24,30,28,35,36); $c=sqrt($a^2+$b^2); condition:eq(int($c),$c); $j=rint(5); $a1=switch($j,24,9,27,14,30); $b1=switch($j,32,40,36,48,40); $c1=sqrt($a1^2+$b1^2); condition:eq(int($c1),$c1); $k=rint(5); $a2=switch($k,24,20,28,33,40); $b2=switch($k,45,48,45,44,42); $c2=sqrt($a2^2+$b2^2); condition:eq(int($c2),$c2);@ qu.11.3.question=Place a check beside each set of sides of a triangle which form a right triangle.@ qu.11.3.answer=1, 2, 3@ qu.11.3.choice.1=a = $a, b = $b, c = $c@ qu.11.3.choice.2=a = $a1, b = $b1, c = $c1@ qu.11.3.choice.3=a = $a2, b = $b2, c = $c2@ qu.12.topic=9_3 Find Leg of Rt. Triangle B@ qu.12.1.question=
?
$c $u
$b $u

Determine the missing length.
Round to the nearest tenth if necessary.

@ qu.12.1.answer.num=$a@ qu.12.1.answer.units=cm@ qu.12.1.showUnits=true@ qu.12.1.grading=exact_value@ qu.12.1.negStyle=minus@ qu.12.1.numStyle=thousands scientific dollars arithmetic@ qu.12.1.mode=Numeric@ qu.12.1.name=Triangle 1@ qu.12.1.comment=
?
$c $u
$b $u

Determine the missing length.
Round to the nearest tenth if necessary.

Use the pythagorean theorem.
a2 + b2 = c2
Substitute
a2 + $b2 = $c2
Evaluate powers
a2 + ${$b^2} = ${$c^2}
Solve for a 2
a2 = ${$c^2-$b^2}
Take the positive square root of both sides.

a =
${$c^2-$b^2}
= $a and the units will be $u
@ qu.12.1.editing=useHTML@ qu.12.1.algorithm=$b=range(10,25,1); $c=range($b+2,$b+10,1); $a=decimal(1,sqrt($c^2-$b^2)); condition:ne(int($a),$a); $u="cm";@ qu.12.2.question=
$b $u
$c $u
?

Determine the missing length.
Round to the nearest tenth if necessary.

@ qu.12.2.answer.num=$a@ qu.12.2.answer.units=ft@ qu.12.2.showUnits=true@ qu.12.2.grading=exact_value@ qu.12.2.negStyle=minus@ qu.12.2.numStyle=thousands scientific dollars arithmetic@ qu.12.2.mode=Numeric@ qu.12.2.name=Triangle 2@ qu.12.2.comment=
$b $u
$c $u
?

Determine the missing length.
Round to the nearest tenth if necessary.

Use the pythagorean theorem.
a2 + b2 = c2
Substitute
a2 + $b2 = $c2
Evaluate powers
a2 + ${$b^2} = ${$c^2}
Solve for a 2
a2 = ${$c^2-$b^2}
Take the positive square root of both sides.

a =
${$c^2-$b^2}
= $a and the units will be $u
@ qu.12.2.editing=useHTML@ qu.12.2.algorithm=$b=range(10,25,1); $c=range($b+2,$b+10,1); $a=decimal(1,sqrt($c^2-$b^2)); condition:ne(int($a),$a); $u="ft";@ qu.12.3.question=
$b $u
$c $u
?

Determine the missing length.
Round to the nearest tenth if necessary.

@ qu.12.3.answer.num=$a@ qu.12.3.answer.units=m@ qu.12.3.showUnits=true@ qu.12.3.grading=exact_value@ qu.12.3.negStyle=minus@ qu.12.3.numStyle=thousands scientific dollars arithmetic@ qu.12.3.mode=Numeric@ qu.12.3.name=Opp Leg Triangle 1@ qu.12.3.comment=
$b $u
$c $u
?

Determine the missing length.
Round to the nearest tenth if necessary.

Use the pythagorean theorem.
a2 + b2 = c2
Substitute
a2 + $b2 = $c2
Evaluate powers
a2 + ${$b^2} = ${$c^2}
Solve for a 2
a2 = ${$c^2-$b^2}
Take the positive square root of both sides.

a =
${$c^2-$b^2}
= $a and the units will be $u
@ qu.12.3.editing=useHTML@ qu.12.3.algorithm=$b=range(10,25,1); $c=range($b+2,$b+10,1); $a=decimal(1,sqrt($c^2-$b^2)); condition:ne(int($a),$a); $u="m";@ qu.12.4.question=
?
$c $u
$b $u

Determine the missing length.
Round to the nearest tenth if necessary.

@ qu.12.4.answer.num=$a@ qu.12.4.answer.units=yd@ qu.12.4.showUnits=true@ qu.12.4.grading=exact_value@ qu.12.4.negStyle=minus@ qu.12.4.numStyle=thousands scientific dollars arithmetic@ qu.12.4.mode=Numeric@ qu.12.4.name=Opp Leg Triangle 2@ qu.12.4.comment=
?
$c $u
$b $u

Determine the missing length.
Round to the nearest tenth if necessary.

Use the pythagorean theorem.
a2 + b2 = c2
Substitute
a2 + $b2 = $c2
Evaluate powers
a2 + ${$b^2} = ${$c^2}
Solve for a 2
a2 = ${$c^2-$b^2}
Take the positive square root of both sides.

a =
${$c^2-$b^2}
= $a and the units will be $u
@ qu.12.4.editing=useHTML@ qu.12.4.algorithm=$b=range(10,25,1); $c=range($b+2,$b+10,1); $a=decimal(1,sqrt($c^2-$b^2)); condition:ne(int($a),$a); $u="yd";@ qu.13.topic=9_3 Find Hyp. of Rt. Triangle B@ qu.13.1.question=
$b $u
?
$a $u

Determine the missing length.
Round to the nearest tenth if necessary.

@ qu.13.1.answer.num=$c@ qu.13.1.answer.units=mm@ qu.13.1.showUnits=true@ qu.13.1.grading=exact_value@ qu.13.1.negStyle=minus@ qu.13.1.numStyle=thousands scientific dollars arithmetic@ qu.13.1.mode=Numeric@ qu.13.1.name=triangle 1@ qu.13.1.comment=
$b $u
?
$a $u

Determine the missing length.
Round to the nearest tenth if necessary.

Pythagorean Theorem
a2 + b2 = c2
Substitute
$a2 + $b2 = c2
Evaluate powers
${$a^2} + ${$b^2} = c2
Add
${$a^2+$b^2} = c2
Take the positive square root of both sides.

c =
${$a^2+$b^2}
= $c and the units would be $u
@ qu.13.1.editing=useHTML@ qu.13.1.algorithm=$a=range(10,25,1); $b=range(10,25,1); $c=decimal(1,sqrt($a^2+$b^2)); condition:ne(int($c),$c); $u="mm";@ qu.13.2.question=
$a $u
?
$b $u

Determine the missing length.
Round to the nearest tenth if necessary.

@ qu.13.2.answer.num=$c@ qu.13.2.answer.units=in@ qu.13.2.showUnits=true@ qu.13.2.grading=exact_value@ qu.13.2.negStyle=minus@ qu.13.2.numStyle=thousands scientific dollars arithmetic@ qu.13.2.mode=Numeric@ qu.13.2.name=triangle 2@ qu.13.2.comment=
$a $u
?
$b $u

Determine the missing length.
Round to the nearest tenth if necessary.

Pythagorean Theorem
a2 + b2 = c2
Substitute
$a2 + $b2 = c2
Evaluate powers
${$a^2} + ${$b^2} = c2
Add
${$a^2+$b^2} = c2
Take the positive square root of both sides.

c =
${$a^2+$b^2}
= $c and the units would be $u
@ qu.13.2.editing=useHTML@ qu.13.2.algorithm=$a=range(10,25,1); $b=range(10,25,1); $c=decimal(1,sqrt($a^2+$b^2)); condition:ne(int($c),$c); $u="in";@ qu.14.topic=9_4 Determine Pythagorean Triple@ qu.14.1.mode=Multiple Selection@ qu.14.1.name=1 correct@ qu.14.1.comment=

Place a check beside each set of numbers which form a pythagorean triple.
For each set of numbers, use the pythagorean theorem to check if The set of numbers is a pythagorean triple.
a2 + b2 = c2

$a, $b, $c
${$a^2} + ${$b^2} ? ${$c^2}
${$a^2+$b^2} ? ${$c^2}
The statement is true. The numbers form a pythagorean triple.

$a1, $b1, $c1
${$a1^2} + ${$b1^2} ? ${$c1^2}
${$a1^2+$b1^2} ? ${$c1^2}
The statement is false. The numbers do not form a pythagorean triple.

$a2, $b2, $c2
${$a2^2} + ${$b2^2} ? ${$c2^2}
${$a2^2+$b2^2} ? ${$c2^2}
The statement is false. The numbers do not form a pythagorean triple.

@ qu.14.1.editing=useHTML@ qu.14.1.algorithm=$i=rint(5); $a=switch($i,18,16,21,12,15); $b=switch($i,24,30,28,35,36); $c=sqrt($a^2+$b^2); condition:eq(int($c),$c); $j=rint(5); $a1=switch($j,24,9,27,14,30); $b1=switch($j,32,40,36,48,40); $c1=sqrt($a1^2+$b1^2)-1; $k=rint(5); $a2=switch($k,24,20,28,33,40); $b2=switch($k,45,48,45,44,42); $c2=sqrt($a2^2+$b2^2)+1;@ qu.14.1.question=Place a check beside each set of numbers which form a pythagorean triple.@ qu.14.1.answer=1@ qu.14.1.choice.1=$a, $b, $c@ qu.14.1.choice.2=$a1, $b1, $c1@ qu.14.1.choice.3=$a2, $b2, $c2@ qu.14.2.mode=Multiple Selection@ qu.14.2.name=2 correct@ qu.14.2.comment=

Place a check beside each set of numbers which form a pythagorean triple.
For each set of numbers, use the pythagorean theorem to check if The set of numbers is a pythagorean triple.
a2 + b2 = c2

$a, $b, $c
${$a^2} + ${$b^2} ? ${$c^2}
${$a^2+$b^2} ? ${$c^2}
The statement is true. The numbers form a pythagorean triple.

$a1, $b1, $c1
${$a1^2} + ${$b1^2} ? ${$c1^2}
${$a1^2+$b1^2} ? ${$c1^2}
The statement is true. The set of numbers is a pythagorean triple.

$a2, $b2, $c2
${$a2^2} + ${$b2^2} ? ${$c2^2}
${$a2^2+$b2^2} ? ${$c2^2}
The statement is false. The numbers do not form a pythagorean triple.

@ qu.14.2.editing=useHTML@ qu.14.2.algorithm=$i=rint(5); $a=switch($i,18,16,21,12,15); $b=switch($i,24,30,28,35,36); $c=sqrt($a^2+$b^2); condition:eq(int($c),$c); $j=rint(5); $a1=switch($j,24,9,27,14,30); $b1=switch($j,32,40,36,48,40); $c1=sqrt($a1^2+$b1^2); condition:eq(int($c1),$c1); $k=rint(5); $a2=switch($k,24,20,28,33,40); $b2=switch($k,45,48,45,44,42); $c2=sqrt($a2^2+$b2^2)+1;@ qu.14.2.question=Place a check beside each set of numbers which form a pythagorean triple.@ qu.14.2.answer=1, 2@ qu.14.2.choice.1=$a, $b, $c@ qu.14.2.choice.2=$a1, $b1, $c1@ qu.14.2.choice.3=$a2, $b2, $c2@ qu.14.3.mode=Multiple Selection@ qu.14.3.name=3 correct@ qu.14.3.comment=

Place a check beside each set of numbers which form a pythagorean triple.
For each set of numbers, use the pythagorean theorem to check if The set of numbers is a pythagorean triple.
a2 + b2 = c2

$a, $b, $c
${$a^2} + ${$b^2} ? ${$c^2}
${$a^2+$b^2} ? ${$c^2}
The statement is true. The numbers form a pythagorean triple.

$a1, $b1, $c1
${$a1^2} + ${$b1^2} ? ${$c1^2}
${$a1^2+$b1^2} ? ${$c1^2}
The statement is true. The set of numbers is a pythagorean triple.

$a2, $b2, $c2
${$a2^2} + ${$b2^2} ? ${$c2^2}
${$a2^2+$b2^2} ? ${$c2^2}
The statement is true. The set of numbers is a pythagorean triple.

@ qu.14.3.editing=useHTML@ qu.14.3.algorithm=$i=rint(5); $a=switch($i,18,16,21,12,15); $b=switch($i,24,30,28,35,36); $c=sqrt($a^2+$b^2); condition:eq(int($c),$c); $j=rint(5); $a1=switch($j,24,9,27,14,30); $b1=switch($j,32,40,36,48,40); $c1=sqrt($a1^2+$b1^2); condition:eq(int($c1),$c1); $k=rint(5); $a2=switch($k,24,20,28,33,40); $b2=switch($k,45,48,45,44,42); $c2=sqrt($a2^2+$b2^2); condition:eq(int($c2),$c2);@ qu.14.3.question=Place a check beside each set of numbers which form a pythagorean triple.@ qu.14.3.answer=1, 2, 3@ qu.14.3.choice.1=$a, $b, $c@ qu.14.3.choice.2=$a1, $b1, $c1@ qu.14.3.choice.3=$a2, $b2, $c2@ qu.15.topic=9_4 Perimeter and Area A@ qu.15.1.mode=Inline@ qu.15.1.name=missing hypotenuse@ qu.15.1.comment=

Find the perimeter and area of the triangle with sides a = $a, b = $b, and c = ?.
Answers should be accurate to the tenths place.
Enter square units such as m2 with a ^ as m^2

Find the hypotenuse.
a2 + b2 = c2
$a2 + $b2 = c2
${$a^2} + ${$b^2} = c2
${$a^2+$b^2} = c2

c =
${$a^2+$b^2}
 = $c


Perimeter is the sum of all of the sides.
P = $a $u + $b $u + $c $u = $p $u

A = ½ • base • height
A = ½ • $a $u • $b $u = $area $u^2

@ qu.15.1.editing=useHTML@ qu.15.1.algorithm=$a=range(10,25,1); $b=range(10,25,1); $c=decimal(1,sqrt($a^2+$b^2)); $u="cm"; $p=$a+$b+$c; $area=.5*$a*$b;@ qu.15.1.weighting=1,1@ qu.15.1.numbering=alpha@ qu.15.1.part.1.name=$p cm@ qu.15.1.part.1.answer.units=cm@ qu.15.1.part.1.numStyle=thousands scientific arithmetic@ qu.15.1.part.1.editing=useHTML@ qu.15.1.part.1.showUnits=true@ qu.15.1.part.1.question=(Unset)@ qu.15.1.part.1.mode=Numeric@ qu.15.1.part.1.grading=exact_value@ qu.15.1.part.1.negStyle=minus@ qu.15.1.part.1.answer.num=$p@ qu.15.1.part.2.name=$area cm^2@ qu.15.1.part.2.answer.units=cm^2@ qu.15.1.part.2.numStyle=thousands scientific arithmetic@ qu.15.1.part.2.editing=useHTML@ qu.15.1.part.2.showUnits=true@ qu.15.1.part.2.question=(Unset)@ qu.15.1.part.2.mode=Numeric@ qu.15.1.part.2.grading=exact_value@ qu.15.1.part.2.negStyle=minus@ qu.15.1.part.2.answer.num=$area@ qu.15.1.question=

Find the perimeter and area of the triangle with sides a = $a $u, b = $b $u, and c = ?.
Answers should be accurate to the tenths place.
Enter square units such as m2 with a ^ as m^2

Perimeter = <1>
Area = <2>

@ qu.15.2.mode=Inline@ qu.15.2.name=missing leg@ qu.15.2.comment=Find the perimeter and area of the triangle with sides a = ?, b = $b, and c = $c.
Round to the nearest tenth if necessary.
Enter square units such as m2 with a ^ as m^2

Find the missing side.
a2 + b2 = c2
a2 + $b2 = $c2
a2 + ${$b^2} = ${$c^2}
a2 = ${$c^2-$b^2}

a =
${$c^2-$b^2}
= $a and the units will be $u

Perimeter is the sum of all of the sides.
P = $a $u + $b $u + $c $u = $p $u

A = ½ • base • height
A = ½ • $a $u • $b $u = $area $u^2

@ qu.15.2.editing=useHTML@ qu.15.2.algorithm=$b=range(10,25,1); $c=$b+range(5,$b-2,1); $a=decimal(1,sqrt($c^2-$b^2)); $u="ft"; $p=$a+$b+$c; $area=decimal(1,.5*$a*$b);@ qu.15.2.weighting=1,1@ qu.15.2.numbering=alpha@ qu.15.2.part.1.name=$p ft@ qu.15.2.part.1.answer.units=ft@ qu.15.2.part.1.numStyle=thousands scientific arithmetic@ qu.15.2.part.1.editing=useHTML@ qu.15.2.part.1.showUnits=true@ qu.15.2.part.1.question=(Unset)@ qu.15.2.part.1.mode=Numeric@ qu.15.2.part.1.grading=exact_value@ qu.15.2.part.1.negStyle=minus@ qu.15.2.part.1.answer.num=$p@ qu.15.2.part.2.name=$area ft^2@ qu.15.2.part.2.answer.units=ft^2@ qu.15.2.part.2.numStyle=thousands scientific arithmetic@ qu.15.2.part.2.editing=useHTML@ qu.15.2.part.2.showUnits=true@ qu.15.2.part.2.question=(Unset)@ qu.15.2.part.2.mode=Numeric@ qu.15.2.part.2.grading=exact_value@ qu.15.2.part.2.negStyle=minus@ qu.15.2.part.2.answer.num=$area@ qu.15.2.question=

Find the perimeter and area of the triangle with sides a = ?, b = $b $u , and c = $c $u .
Round to the nearest tenth if necessary.
Enter square units such as m2 with a ^ as m^2

Perimeter = <1>
Area = <2>

@ qu.16.topic=9_4 Perimeter and Area B@ qu.16.1.mode=Inline@ qu.16.1.name=Missing leg@ qu.16.1.comment=
$b $u
$c $u
?

Find the perimeter and area of the triangle.
Round to the nearest tenth if necessary.

Find the missing side.
a2 + b2 = c2
a2 + $b2 = $c2
a2 + ${$b^2} = ${$c^2}
a2 = ${$c^2-$b^2}

a =
${$c^2-$b^2}
= $a and the units will be $u

Perimeter is the sum of all of the sides.
P = $a $u + $b $u + $c $u = $p $u

A = ½ • base • height
A = ½ • $a $u • $b $u = $area $u^2

@ qu.16.1.editing=useHTML@ qu.16.1.algorithm=$b=range(10,25,1); $c=$b+range(5,$b-2,1); $a=decimal(1,sqrt($c^2-$b^2)); $u="in"; $p=$a+$b+$c; $area=decimal(1,.5*$a*$b);@ qu.16.1.weighting=1,1@ qu.16.1.numbering=alpha@ qu.16.1.part.1.name=$p in@ qu.16.1.part.1.answer.units=in@ qu.16.1.part.1.numStyle=thousands scientific arithmetic@ qu.16.1.part.1.editing=useHTML@ qu.16.1.part.1.showUnits=true@ qu.16.1.part.1.question=(Unset)@ qu.16.1.part.1.mode=Numeric@ qu.16.1.part.1.grading=exact_value@ qu.16.1.part.1.negStyle=minus@ qu.16.1.part.1.answer.num=$p@ qu.16.1.part.2.name=$area in^2@ qu.16.1.part.2.answer.units=in^2@ qu.16.1.part.2.numStyle=thousands scientific arithmetic@ qu.16.1.part.2.editing=useHTML@ qu.16.1.part.2.showUnits=true@ qu.16.1.part.2.question=(Unset)@ qu.16.1.part.2.mode=Numeric@ qu.16.1.part.2.grading=exact_value@ qu.16.1.part.2.negStyle=minus@ qu.16.1.part.2.answer.num=$area@ qu.16.1.question=
$b $u 
$c $u 
?

Find the perimeter and area of the triangle.
Round to the nearest tenth if necessary.
Enter square units such as m2 with a ^ as m^2

Perimeter = <1>
Area = <2>

@ qu.16.2.mode=Inline@ qu.16.2.name=missing hypotenuse@ qu.16.2.comment=
$b $u
?
$a $u

Find the perimeter and area of the triangle.
Answers should be accurate to the tenths place.
Enter square units such as m2 with a ^ as m^2

Find the hypotenuse.
a2 + b2 = c2
$a2 + $b2 = c2
${$a^2} + ${$b^2} = c2
${$a^2+$b^2} = c2

c =
${$a^2+$b^2}
 = $c


Perimeter is the sum of all of the sides.
P = $a $u + $b $u + $c $u = $p $u

A = ½ • base • height
A = ½ • $a $u • $b $u = $area $u^2

@ qu.16.2.editing=useHTML@ qu.16.2.algorithm=$a=range(10,25,1); $b=range(10,25,1); $c=decimal(1,sqrt($a^2+$b^2)); $u="m"; $p=$a+$b+$c; $area=.5*$a*$b;@ qu.16.2.weighting=1,1@ qu.16.2.numbering=alpha@ qu.16.2.part.1.name=$p m@ qu.16.2.part.1.answer.units=m@ qu.16.2.part.1.numStyle=thousands scientific arithmetic@ qu.16.2.part.1.editing=useHTML@ qu.16.2.part.1.showUnits=true@ qu.16.2.part.1.question=(Unset)@ qu.16.2.part.1.mode=Numeric@ qu.16.2.part.1.grading=exact_value@ qu.16.2.part.1.negStyle=minus@ qu.16.2.part.1.answer.num=$p@ qu.16.2.part.2.name=$area m^2@ qu.16.2.part.2.answer.units=m^2@ qu.16.2.part.2.numStyle=thousands scientific arithmetic@ qu.16.2.part.2.editing=useHTML@ qu.16.2.part.2.showUnits=true@ qu.16.2.part.2.question=(Unset)@ qu.16.2.part.2.mode=Numeric@ qu.16.2.part.2.grading=exact_value@ qu.16.2.part.2.negStyle=minus@ qu.16.2.part.2.answer.num=$area@ qu.16.2.question=
$b $u
?
$a $u

Find the perimeter and area of the triangle.
Answers should be accurate to the tenths place.
Enter square units such as m2 with a ^ as m^2

Perimeter = <1>
Area = <2>

@ qu.17.topic=9_4 Perimeter and Area C@ qu.17.1.question=

Find the perimeter of the triangle.
Round all decimals to 1 decimal place where necessary.

Area = $area $u2, a = $a $u

@ qu.17.1.answer.num=$p@ qu.17.1.answer.units=m@ qu.17.1.showUnits=true@ qu.17.1.grading=exact_value@ qu.17.1.negStyle=minus@ qu.17.1.numStyle=thousands scientific dollars arithmetic@ qu.17.1.mode=Numeric@ qu.17.1.name=Perimeter given area@ qu.17.1.comment=

Find the perimeter of the triangle.
Round all decimals to 1 decimal place where necessary.

Area = $area $u2, a = $a $u

Use the area to find side b.
Area = ½ • base • height
$area $u2 = ½ • $a $u • b
$area $u2 = ${.5*$a} $u • b
$b $u = b

Find the hypotenuse.
a2 + b2 = c2
$a2 + $b2 = c2
${$a^2} + ${$b^2} = c2
${$a^2+$b^2} = c2

c =
${$a^2+$b^2}
 = $c

Perimeter = sum of all of the sides
P = $a $u + $b $u + $c $u
P = $p $u

@ qu.17.1.editing=useHTML@ qu.17.1.algorithm=$a=range(3,8,1); $area=range(20,40,1); $b=decimal(1,2*$area/$a); $c=decimal(1,sqrt($a^2+$b^2)); $p=$a+$b+$c; $u="m";@ qu.18.topic=9_4 Word Problems@ qu.18.1.question=

A $a ft vertical pole has a wire running from the top of the pole to a point on the ground $b ft from the base of the pole. The cable must be ordered by the foot. How many feet will be required?

@ qu.18.1.answer.num=$ans@ qu.18.1.answer.units=@ qu.18.1.showUnits=false@ qu.18.1.grading=exact_value@ qu.18.1.negStyle=minus@ qu.18.1.numStyle=thousands scientific dollars arithmetic@ qu.18.1.mode=Numeric@ qu.18.1.name=pole@ qu.18.1.comment=

A $a ft vertical pole has a wire running from the top of the pole to a point on the ground $b ft from the base of the pole. The cable must be ordered by the foot. How many feet will be required?

The height h of the pole is $a ft. The distance b from the base of the pole is $b ft. The cable length c is the hypotenuse of the right triangle. Use the Pythagorean theorem to find the length of the cable c.

Find the hypotenuse.
a2 + b2 = c2
$a2 + $b2 = c2
${$a^2} + ${$b^2} = c2
${$a^2+$b^2} = c2
c = $c ft

The length of the must be in whole feet longer than the distance from the top of the pole to the ground. $ans ft must be purchased.

@ qu.18.1.editing=useHTML@ qu.18.1.algorithm=$a=range(15,35,1); $b=range(8,12,1); $c=sqrt($a^2+$b^2); condition:ne(int($c),$c); $ans=int($c)+1;@ qu.18.2.question=

Surveyors are trying to estimate the area of Welkerville Lake shown in the diagram at the left. The length of W Shore Dr. is $a ft. The length of S Shore Dr. is $b ft. To the nearest square foot, what is the area of the lake?
@ qu.18.2.answer.num=$ans@ qu.18.2.answer.units=@ qu.18.2.showUnits=false@ qu.18.2.grading=exact_value@ qu.18.2.negStyle=minus@ qu.18.2.numStyle=thousands scientific dollars arithmetic@ qu.18.2.mode=Numeric@ qu.18.2.name=lake@ qu.18.2.comment=

Surveyors are trying to estimate the area of Welkerville Lake shown in the diagram at the left. The length of W Shore Dr. is $a ft. The length of S Shore Dr. is $b ft. To the nearest square foot, what is the area of the lake?

Area = ½ • base • height
Area = ½ • $b • $a
Area = ${.5*$b*$a}
To the nearest square foot, the lake is $ans ft2
@ qu.18.2.editing=useHTML@ qu.18.2.algorithm=$a=range(3000,4000,10); $b=range(5000,6000,10); $ans=decimal(0,.5*$a*$b);@ qu.18.3.question=

A balloon is tethered to the ground by a $c m rope. The wind is blowing the balloon to the side. An observer measures the distance from the point where the rope attaches to the ground to a point directly under the balloon to be $b m. To the nearest tenth of a meter, how high above the ground is the balloon?

 
@ qu.18.3.answer.num=$ans@ qu.18.3.answer.units=@ qu.18.3.showUnits=false@ qu.18.3.grading=exact_value@ qu.18.3.negStyle=minus@ qu.18.3.numStyle=thousands scientific dollars arithmetic@ qu.18.3.mode=Numeric@ qu.18.3.name=balloon@ qu.18.3.comment=

A balloon is tethered to the ground by a $c m rope. The wind is blowing the balloon to the side. An observer measures the distance from the point where the rope attaches to the ground to a point directly under the balloon to be $b m. To the nearest tenth of a meter, how high above the ground is the balloon?

Find the height.
a2 + b2 = c2
a2 + $b2 = $c2
a2 + ${$b^2} = ${$c^2}
a2 = ${$c^2-$b^2}
a = $ans m
@ qu.18.3.editing=useHTML@ qu.18.3.algorithm=$c=range(10,30,2); $b=range(2,$c/3,.1); $ans=decimal(1,sqrt($c^2-$b^2));@