Measurement, NAPX9-TLD-CA22 v3

Question

{{{question}}}

Worked Solution

{{{workedSolution}}}

Variant 0

DifficultyLevel

688

Question

The length of this rectangle is three times its height.



The perimeter of the rectangle is 32 centimetres.

What is the area of the rectangle?

Worked Solution
Let  h\ \large h = height
3h3\large h = length
2×(h2 \times (\large h + 3h\large h) = 32
8h8\large h = 32
h\large h = 4
∴\therefore Area = 4 ×\times 12
= 48 cm2^2

Question Type

Answer Box

Variables

Variable nameVariable value
question
The length of this rectangle is three times its height.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement-NAPX9-TLD-CA22-v3_0_1_a.svg 400 indent vpad
The perimeter of the rectangle is 32 centimetres. What is the area of the rectangle?
workedSolution
||| |-:|-| |Let $\ \large h$| = height| |$3\large h$|= length|
||| |-:|-| |$2 \times (\large h$ + 3$\large h$)| = 32| |$8\large h$|= 32| |$\large h$|= 4|
||| |-|-| |$\therefore$ Area| = 4 $\times$ 12| | |= {{{correctAnswer0}}} {{{suffix0}}}|
correctAnswer0
48
prefix0
suffix0
cm$^2$

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer048

cm2^2

Variant 1

DifficultyLevel

685

Question

The length of this rectangle is twice its height.



The perimeter of the rectangle is 30 centimetres.

What is the area of the rectangle?

Worked Solution
Let  h\ \large h = height
2h2\large h = length
2×(h2 \times (\large h + 2h\large h) = 30
6h6\large h = 30
h\large h = 5
∴\therefore Area = 5 ×\times 10
= 50 cm2^2

Question Type

Answer Box

Variables

Variable nameVariable value
question
The length of this rectangle is twice its height.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement-NAPX9-TLD-CA22-v3_0_1_a.svg 400 indent3 vpad
The perimeter of the rectangle is 30 centimetres. What is the area of the rectangle?
workedSolution
||| |-:|-| |Let $\ \large h$| = height| |$2\large h$|= length|
||| |-:|-| |$2 \times (\large h$ + 2$\large h$)| = 30| |$6\large h$|= 30| |$\large h$|= 5|
||| |-|-| |$\therefore$ Area| = 5 $\times$ 10| | |= {{{correctAnswer0}}} {{{suffix0}}}|
correctAnswer0
50
prefix0
suffix0
cm$^2$

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer050

cm2^2

Variant 2

DifficultyLevel

690

Question

The length of this rectangle is one third its height.



The perimeter of the rectangle is 72 centimetres.

What is the area of the rectangle?

Worked Solution
Let  l\ \large l = length
3l3\large l = height
2×(l2 \times (\large l + 3l\large l) = 72
8l8\large l = 72
l\large l = 9
∴\therefore Area = 9 ×\times 27
= 243 cm2^2

Question Type

Answer Box

Variables

Variable nameVariable value
question
The length of this rectangle is one third its height.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement-NAPX9-TLD-CA22-v3_2_3.svg 240 indent3 vpad
The perimeter of the rectangle is 72 centimetres. What is the area of the rectangle?
workedSolution
||| |-:|-| |Let $\ \large l$| = length| |$3\large l$|= height|
||| |-:|-| |$2 \times (\large l$ + 3$\large l$)| = 72| |$8\large l$|= 72| |$\large l$|= 9|
||| |-|-| |$\therefore$ Area| = 9 $\times$ 27| | |= {{{correctAnswer0}}} {{{suffix0}}}|
correctAnswer0
243
prefix0
suffix0
cm$^2$

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer0243

cm2^2

Variant 3

DifficultyLevel

693

Question

The length of this rectangle is one-quarter its height.



The perimeter of the rectangle is 50 centimetres.

What is the area of the rectangle?

Worked Solution
Let  l\ \large l = length
4l4\large l = height
2×(l2 \times (\large l + 4l\large l) = 50
10l10\large l = 50
l\large l = 5
∴\therefore Area = 5 ×\times 20
= 100 cm2^2

Question Type

Answer Box

Variables

Variable nameVariable value
question
The length of this rectangle is one-quarter its height.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement-NAPX9-TLD-CA22-v3_2_3.svg 240 indent3 vpad
The perimeter of the rectangle is 50 centimetres. What is the area of the rectangle?
workedSolution
||| |-:|-| |Let $\ \large l$| = length| |$4\large l$|= height|
||| |-:|-| |$2 \times (\large l$ + 4$\large l$)| = 50| |$10\large l$|= 50| |$\large l$|= 5|
||| |-|-| |$\therefore$ Area| = 5 $\times$ 20| | |= {{{correctAnswer0}}} {{{suffix0}}}|
correctAnswer0
100
prefix0
suffix0
cm$^2$

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer0100

cm2^2

Variant 4

DifficultyLevel

694

Question

The length of this rectangle is one and a half times its height.



The perimeter of the rectangle is 60 centimetres.

What is the area of the rectangle?

Worked Solution
Let  h\ \large h = height
1.5h1.5\large h = length
2×(h2 \times (\large h + 1.5h\large h) = 60
5h5\large h = 60
h\large h = 12
∴\therefore Area = 12 ×\times 18
= 216 cm2^2

Question Type

Answer Box

Variables

Variable nameVariable value
question
The length of this rectangle is one and a half times its height.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement-NAPX9-TLD-CA22-v3_4_5.svg 300 indent vpad
The perimeter of the rectangle is 60 centimetres. What is the area of the rectangle?
workedSolution
||| |-:|-| |Let $\ \large h$| = height| |$1.5\large h$|= length|
||| |-:|-| |$2 \times (\large h$ + 1.5$\large h$)| = 60| |$5\large h$|= 60| |$\large h$|= 12|
||| |-|-| |$\therefore$ Area| = 12 $\times$ 18| | |= {{{correctAnswer0}}} {{{suffix0}}}|
correctAnswer0
216
prefix0
suffix0
cm$^2$

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer0216

cm2^2

Variant 5

DifficultyLevel

692

Question

The length of this rectangle is two and half times its height.



The perimeter of the rectangle is 42 centimetres.

What is the area of the rectangle?

Worked Solution
Let  h\ \large h = height
2.5h2.5\large h = length
2×(h2 \times (\large h + 2.5h\large h) = 42
7h7\large h = 42
h\large h = 6
∴\therefore Area = 6 ×\times 15
= 90 cm2^2

Question Type

Answer Box

Variables

Variable nameVariable value
question
The length of this rectangle is two and half times its height.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Measurement-NAPX9-TLD-CA22-v3_4_5.svg 300 indent vpad
The perimeter of the rectangle is 42 centimetres. What is the area of the rectangle?
workedSolution
||| |-:|-| |Let $\ \large h$| = height| |$2.5\large h$|= length|
||| |-:|-| |$2 \times (\large h$ + 2.5$\large h$)| = 42| |$7\large h$|= 42| |$\large h$|= 6|
||| |-|-| |$\therefore$ Area| = 6 $\times$ 15| | |= {{{correctAnswer0}}} {{{suffix0}}}|
correctAnswer0
90
prefix0
suffix0
cm$^2$

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer090

cm2^2

Tags

  • ms_ca