20315

Question

{{{question}}}

Worked Solution

{{{workedSolution}}}

Variant 0

DifficultyLevel

580

Question

A rectangle has a length of 20 cm and a width of 12 cm.

A square has the same perimeter as this rectangle.

What is the side length of this square in centimetres?

Worked Solution
Perimeter of rectangle = (2 ×\times 12) + (2 ×\times 20)
= 64 cm

Side length of square = 644\dfrac{64}{4}
= 16 cm

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
A rectangle has a length of 20 cm and a width of 12 cm. A square has the same perimeter as this rectangle. What is the side length of this square in centimetres?
workedSolution
| | | | --------------------- | -------------------------------------------- | | Perimeter of rectangle | = (2 $\times$ 12) + (2 $\times$ 20) | | | = 64 cm |

| | | | --------------------- | -------------------------------------------- | | Side length of square | = $\dfrac{64}{4}$ | | | = {{{correctAnswer}}} |
correctAnswer
16 cm

Answers

Is Correct?Answer
x

8 cm

x

11.25 cm

✓

16 cm

x

32 cm

Variant 1

DifficultyLevel

579

Question

A rectangle has a length of 41.5 cm and a width of 19 cm.

A square has the same perimeter as this rectangle.

What is the side length of this square in centimetres?

Worked Solution
Perimeter of rectangle = (2 ×\times 41.5) + (2 ×\times 19)
= 121 cm

Side length of square = 1214\dfrac{121}{4}
= 30.25 cm

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
A rectangle has a length of 41.5 cm and a width of 19 cm. A square has the same perimeter as this rectangle. What is the side length of this square in centimetres?
workedSolution
| | | | --------------------- | -------------------------------------------- | | Perimeter of rectangle | = (2 $\times$ 41.5) + (2 $\times$ 19) | | | = 121 cm |

| | | | --------------------- | -------------------------------------------- | | Side length of square | = $\dfrac{121}{4}$ | | | = {{{correctAnswer}}} |
correctAnswer
30.25 cm

Answers

Is Correct?Answer
x

11 cm

✓

30.25 cm

x

61.5 cm

x

199.5 cm

Variant 2

DifficultyLevel

578

Question

A rectangle has a length of 31 cm and a width of 53.5 cm.

A square has the same perimeter as this rectangle.

What is the side length of this square in centimetres?

Worked Solution
Perimeter of rectangle = (2 ×\times 31) + (2 ×\times 53.5)
= 169 cm

Side length of square = 1694\dfrac{169}{4}
= 42.25 cm

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
A rectangle has a length of 31 cm and a width of 53.5 cm. A square has the same perimeter as this rectangle. What is the side length of this square in centimetres?
workedSolution
| | | | --------------------- | -------------------------------------------- | | Perimeter of rectangle | = (2 $\times$ 31) + (2 $\times$ 53.5) | | | = 169 cm |

| | | | --------------------- | -------------------------------------------- | | Side length of square | = $\dfrac{169}{4}$ | | | = {{{correctAnswer}}} |
correctAnswer
42.25 cm

Answers

Is Correct?Answer
x

13 cm

x

21.5

✓

42.25 cm

x

84.5 cm

Variant 3

DifficultyLevel

577

Question

A rectangle has a length of 9 cm and a width of 31.5 cm.

A square has the same perimeter as this rectangle.

What is the side length of this square in centimetres?

Worked Solution
Perimeter of rectangle = (2 ×\times 9) + (2 ×\times 31.5)
= 81 cm

Side length of square = 814\dfrac{81}{4}
= 20.25 cm

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
A rectangle has a length of 9 cm and a width of 31.5 cm. A square has the same perimeter as this rectangle. What is the side length of this square in centimetres?
workedSolution
| | | | --------------------- | -------------------------------------------- | | Perimeter of rectangle | = (2 $\times$ 9) + (2 $\times$ 31.5) | | | = 81 cm |

| | | | --------------------- | -------------------------------------------- | | Side length of square | = $\dfrac{81}{4}$ | | | = {{{correctAnswer}}} |
correctAnswer
20.25 cm

Answers

Is Correct?Answer
x

9 cm

x

10 cm

✓

20.25 cm

x

40.5 cm

Variant 4

DifficultyLevel

584

Question

A rectangular paddock has a length of 140 m and a width of 102 m.

An adjoining paddock is a square and has the same perimeter as the rectangular paddock.

What is the side length of the square paddock in metres?

Worked Solution
Perimeter of rectangular paddock = (2 ×\times 140) + (2 ×\times 102)
= 484 m

Side length of square paddock = 4844\dfrac{484}{4}
= 121 m

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
A rectangular paddock has a length of 140 m and a width of 102 m. An adjoining paddock is a square and has the same perimeter as the rectangular paddock. What is the side length of the square paddock in metres?
workedSolution
| | | | --------------------- | -------------------------------------------- | | Perimeter of rectangular paddock | = (2 $\times$ 140) + (2 $\times$ 102) | | | = 484 m |

| | | | --------------------- | -------------------------------------------- | | Side length of square paddock | = $\dfrac{484}{4}$ | | | = {{{correctAnswer}}} |
correctAnswer
121 m

Answers

Is Correct?Answer
x

22 m

✓

121 m

x

242 m

x

1840 m

Variant 5

DifficultyLevel

582

Question

A rectangular table has a length of 2.8 m and a width of 1.2 m.

A square table has the same perimeter as the rectangular table.

What is the side length of the square table in metres?

Worked Solution
Perimeter of rectangular paddock = (2 ×\times 2.8) + (2 ×\times 1.2)
= 8 m

Side length of square paddock = 84\dfrac{8}{4}
= 2 m

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
A rectangular table has a length of 2.8 m and a width of 1.2 m. A square table has the same perimeter as the rectangular table. What is the side length of the square table in metres?
workedSolution
| | | | --------------------- | -------------------------------------------- | | Perimeter of rectangular paddock | = (2 $\times$ 2.8) + (2 $\times$ 1.2) | | | = 8 m |

| | | | --------------------- | -------------------------------------------- | | Side length of square paddock | = $\dfrac{8}{4}$ | | | = {{{correctAnswer}}} |
correctAnswer
2 m

Answers

Is Correct?Answer
✓

2 m

x

3.36 m

x

4 m

x

8 m

Tags

  • ms_ca