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Similar shapes: lengths practice questions with answers

Foundation and Higher · Grade 5

A second set of similar shapes: lengths questions for GCSE Maths. They are different from the ones on the topic page, so work through both. Try each question, then open the answer to check your working.

More questions

Question 1 Easy

A shape is enlarged by length scale factor 5. A side of 3 cm becomes what length?

Show answer

Answer: 15

  1. Multiply side by scale factor: 5 × 3.
  2. Result is 15.
  • Method (1): Multiply side by scale factor: 5 × 3.
  • Accuracy (1): Result is 15.

Question 2 Easy

A shape is enlarged by length scale factor 3. A side of 6 cm becomes what length?

Show answer

Answer: 18

  1. Multiply side by scale factor: 3 × 6.
  2. Result is 18.
  • Method (1): Multiply side by scale factor: 3 × 6.
  • Accuracy (1): Result is 18.

Question 3 Medium

A shape is shrunk by length scale factor 1/4. A side of 12 cm becomes what length?

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Answer: 3

  1. Multiply side by scale factor: (1/4) × 12.
  2. Result is 3.
  • Method (1): Multiply side by scale factor: (1/4) × 12.
  • Accuracy (1): Result is 3.

Question 4 Medium

A shape is shrunk by length scale factor 1/2. A side of 14 cm becomes what length?

Show answer

Answer: 7

  1. Multiply side by scale factor: (1/2) × 14.
  2. Result is 7.
  • Method (1): Multiply side by scale factor: (1/2) × 14.
  • Accuracy (1): Result is 7.

Question 5 Hard

A map has scale 1:200. A length of 5 cm on the map is what real length, in cm?

Show answer

Answer: 1000

  1. Multiply by map ratio: 5 × 200.
  2. Result is 1000.
  • Method (1): Multiply by map ratio: 5 × 200.
  • Accuracy (1): Result is 1000.

Question 6 Hard

A map has scale 1:25. A length of 8 cm on the map is what real length, in cm?

Show answer

Answer: 200

  1. Multiply by map ratio: 8 × 25.
  2. Result is 200.
  • Method (1): Multiply by map ratio: 8 × 25.
  • Accuracy (1): Result is 200.

Exam-style question

A longer question with marks, in the style of a written paper. This is a Yumio practice question, not a past paper question.

Exam-style question 12 marks

A map has scale 1:20. A length of 6 cm on the map is what real length, in cm?

Show answer

Answer: 120

  1. Scale ratio 1:20 means 1 cm represents 20 cm.
  2. Multiply map distance by 20: 6 × 20 = 120.
  • Method (1): 6 × 20
  • Accuracy (1): 120

Quick checks

Short one-step questions. Pick an option before you open the answer.

Check 1

What does a length scale factor of k do to side lengths?

  1. Multiplies every length by k
  2. Adds k to every length
  3. Squares every length
Show answer

Multiplies every length by k Similarity preserves shape by multiplying all linear dimensions by k.

Check 2

A side of 4 is enlarged by scale factor 3. What is the new side length?

  1. 12
  2. 7
  3. 4
Show answer

12 4 × 3 = 12.

Check 3

A side of 5 is enlarged by scale factor 4. What is the new side length?

  1. 20
  2. 9
  3. 25
Show answer

20 5 × 4 = 20.

Check 4

A side of 10 is scaled by factor 1/2. What is the new length?

  1. 5
  2. 20
  3. 8
Show answer

5 10 × (1/2) = 5.

Check 5

A side of 9 is scaled by factor 1/3. What is the new length?

  1. 3
  2. 27
  3. 6
Show answer

3 9 × (1/3) = 3.

Check 6

Two similar shapes have corresponding sides 4 cm and 12 cm. What is the scale factor from smaller to larger?

  1. 3
  2. 8
  3. 4
Show answer

3 12 ÷ 4 = 3.

Check 7

Two similar shapes have corresponding sides 6 cm and 18 cm. What is the scale factor from smaller to larger?

  1. 3
  2. 12
  3. 2.5
Show answer

3 18 ÷ 6 = 3.

Check 8

On a map with scale 1:100, what is the real distance of a 3 cm line?

  1. 300 cm
  2. 103 cm
  3. 33 cm
Show answer

300 cm 3 × 100 = 300 cm.

Check 9

On a map with scale 1:50, what is the real distance of a 4 cm line?

  1. 200 cm
  2. 54 cm
  3. 12.5 cm
Show answer

200 cm 4 × 50 = 200 cm.

Check 10

On a map with scale 1:200, what is the real distance of a 5 cm line?

  1. 1000 cm
  2. 205 cm
  3. 40 cm
Show answer

1000 cm 5 × 200 = 1000 cm.

Check 11

Why is adding a scale factor incorrect?

  1. Adding changes the shape proportions
  2. Because lengths cannot be added
  3. It is only allowed for area
Show answer

Adding changes the shape proportions Adding a constant changes the ratio between sides, distorting the shape.

Check 12

What does a scale factor between 0 and 1 represent?

  1. A reduction (shrink)
  2. An enlargement
  3. A reflection
Show answer

A reduction (shrink) A factor less than 1 reduces all linear dimensions.

Check 13

A side of 7 is enlarged by scale factor 2. What is the new side length?

  1. 14
  2. 9
  3. 12
Show answer

14 7 × 2 = 14.

Check 14

On a map with scale 1:25, what is the real distance of a line of length 8 cm?

  1. 200 cm
  2. 33 cm
  3. 2000 cm
Show answer

200 cm 8 × 25 = 200 cm.

Check 15

How do you find the scale factor between two similar shapes?

  1. Divide corresponding side of image by original
  2. Subtract original from image
  3. Multiply the two sides
Show answer

Divide corresponding side of image by original Scale factor k = Image side / Original side.

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