Algebra, NAPX-H4-NC31 SA

Question

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Worked Solution

{{{workedSolution}}}

Variant 0

DifficultyLevel

790

Question

Matilda created a shape using equilateral triangles and squares.

She begins by using a triangle with side length 1 cm.

She then adds a square, then another triangle, then a square etc... until she has a shape with a perimeter of 24 cm.



What is the total number of triangles and squares combined that Matilda has used?

Worked Solution

Perimeter of 1 triangle = 3 cm.

Add a square, perimeter increases by 2 cm

Add a triangle, perimeter increases by 1 cm

⇒\Rightarrow Total perimeter increases as follows:

3,5,6,8,9,11,12,14,15,17,18,20,21,23,243,5,6,8,9,11,12,14,15,17,18,20,21,23,24


∴\therefore 15 triangles and squares (combined) are used.

Question Type

Answer Box

Variables

Variable nameVariable value
question
Matilda created a shape using equilateral triangles and squares. She begins by using a triangle with side length 1 cm. She then adds a square, then another triangle, then a square etc... until she has a shape with a perimeter of 24 cm.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2016/12/NAP-H4-NC31.png 600 indent vpad
What is the total number of triangles and squares combined that Matilda has used?
workedSolution
Perimeter of 1 triangle = 3 cm. Add a square, perimeter increases by 2 cm Add a triangle, perimeter increases by 1 cm $\Rightarrow$ Total perimeter increases as follows: >>$3,5,6,8,9,11,12,14,15,17,18,20,21,23,24$
$\therefore$ {{{correctAnswer0}}} triangles and squares (combined) are used.
correctAnswer0
15
prefix0
suffix0

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
correctAnswer015

Variant 1

DifficultyLevel

771

Question

Bella created a shape using squares and regular pentagons.

She begins by using a square with side length 1 cm.

She then adds a pentagon, then another square, then a pentagon etc... until she has a shape with a perimeter of 22 cm.



What is the total number of squares and pentagons combined that Bella has used?

Worked Solution

Perimeter of 1 square = 4 cm.

Add a pentagon, perimeter increases by 3 cm

Add a square, perimeter increases by 2 cm

⇒\Rightarrow Total perimeter increases as follows:

4,7,9,12,14,17,19,224,7,9,12,14,17,19,22


∴\therefore 8 squares and pentagons (combined) are used.

Question Type

Answer Box

Variables

Variable nameVariable value
question
Bella created a shape using squares and regular pentagons. She begins by using a square with side length 1 cm. She then adds a pentagon, then another square, then a pentagon etc... until she has a shape with a perimeter of 22 cm.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Algebra_NAPX-H4-NC31-SA_v1.svg 500 indent vpad
What is the total number of squares and pentagons combined that Bella has used?
workedSolution
Perimeter of 1 square = 4 cm. Add a pentagon, perimeter increases by 3 cm Add a square, perimeter increases by 2 cm $\Rightarrow$ Total perimeter increases as follows: >>$4,7,9,12,14,17,19,22$
$\therefore$ {{{correctAnswer0}}} squares and pentagons (combined) are used.
correctAnswer0
8
prefix0
suffix0

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
correctAnswer08

Variant 2

DifficultyLevel

782

Question

Barney created a shape using squares and equilateral triangles.

He begins by using a square with side length 1 cm.

He then adds two triangles, then another square, then two triangles etc... until he has a shape with a perimeter of 22 cm.



What is the total number of squares and triangles combined that Barney has used?

Worked Solution

Perimeter of 1 square = 4 cm.

Add 2 triangles, perimeter increases by 2 cm

Add a square, perimeter increases by 2 cm

⇒\Rightarrow Total perimeter increases as follows:

4,6,8,10,12,14,16,18,20,224,6,8,10,12,14,16,18,20,22


Perimeter 4 6 8 ... 20 22
Total squares and triangles 1 3 4 ... 13 15

∴\therefore 15 squares and triangles (combined) are used.

Question Type

Answer Box

Variables

Variable nameVariable value
question
Barney created a shape using squares and equilateral triangles. He begins by using a square with side length 1 cm. He then adds two triangles, then another square, then two triangles etc... until he has a shape with a perimeter of 22 cm.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Algebra_NAPX-H4-NC31-SA_v2.svg 500 indent vpad
What is the total number of squares and triangles combined that Barney has used?
workedSolution
Perimeter of 1 square = 4 cm. Add 2 triangles, perimeter increases by 2 cm Add a square, perimeter increases by 2 cm $\Rightarrow$ Total perimeter increases as follows: >>$4,6,8,10,12,14,16,18,20,22$

>>| Perimeter | 4 |6|8|...|20|22| |:-:|:-:|:-:|:-:|:-:|:-:|:-:| | Total squares and triangles| 1|3|4|...|13|15|

$\therefore$ {{{correctAnswer0}}} squares and triangles (combined) are used.
correctAnswer0
15
prefix0
suffix0

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
correctAnswer015

Variant 3

DifficultyLevel

784

Question

Asti created a shape using regular hexagons and squares.

She begins by using a regular hexagon with side length 1 cm.

She then adds a square, then another hexagon, then a square etc... until she has a shape with a perimeter of 36 cm.



What is the total number of hexagons and squares combined that Asti has used?

Worked Solution

Perimeter of 1 hexagon = 6 cm.

Add a square, perimeter increases by 2 cm

Add a hexagon, perimeter increases by 4 cm

⇒\Rightarrow Total perimeter increases as follows:

6,8,12,14,18,20,24,26,30,32,366,8,12,14,18,20,24,26,30,32,36


∴\therefore 11 hexagons and squares (combined) are used.

Question Type

Answer Box

Variables

Variable nameVariable value
question
Asti created a shape using regular hexagons and squares. She begins by using a regular hexagon with side length 1 cm. She then adds a square, then another hexagon, then a square etc... until she has a shape with a perimeter of 36 cm.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Algebra_J-NAPX-H4-NC31-SA_3.svg 600 indent vpad
What is the total number of hexagons and squares combined that Asti has used?
workedSolution
Perimeter of 1 hexagon = 6 cm. Add a square, perimeter increases by 2 cm Add a hexagon, perimeter increases by 4 cm $\Rightarrow$ Total perimeter increases as follows: >>$6,8,12,14,18,20,24,26,30,32,36$
$\therefore$ {{{correctAnswer0}}} hexagons and squares (combined) are used.
correctAnswer0
11
prefix0
suffix0

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
correctAnswer011

Variant 4

DifficultyLevel

788

Question

Carter created a shape using regular pentagons and squares.

He begins by using a regular pentagon with side length 1 cm.

He then adds a square, then another regular pentagon, then a square etc... until he has a shape with a perimeter of 40 cm.



What is the total number of regular pentagons and squares combined that Carter has used?

Worked Solution

Perimeter of 1 pentagon = 5 cm.

Add a square, perimeter increases by 2 cm

Add a pentagon, perimeter increases by 3 cm

⇒\Rightarrow Total perimeter increases as follows:

5,7,10,12,15,17,20,22,25,27,30,32,35,37,40,425,7,10,12,15,17,20,22,25,27,30,32,35,37,40,42


∴\therefore 16 pentagons and squares (combined) are used.

Question Type

Answer Box

Variables

Variable nameVariable value
question
Carter created a shape using regular pentagons and squares. He begins by using a regular pentagon with side length 1 cm. He then adds a square, then another regular pentagon, then a square etc... until he has a shape with a perimeter of 40 cm.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/Algebra_J-NAPX-H4-NC31-SA_4.svg 660 indent vpad
What is the total number of regular pentagons and squares combined that Carter has used?
workedSolution
Perimeter of 1 pentagon = 5 cm. Add a square, perimeter increases by 2 cm Add a pentagon, perimeter increases by 3 cm $\Rightarrow$ Total perimeter increases as follows: >>$5,7,10,12,15,17,20,22,25,27,30,32,35,37,40,42$
$\therefore$ {{{correctAnswer0}}} pentagons and squares (combined) are used.
correctAnswer0
16
prefix0
suffix0

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
correctAnswer016

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