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Scale factor problems

Scale factor problems

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Summary

Scale factor problems

​​In a nutshell

Scale factor problems involve similar shapes. They allow enlargements to be made whilst keeping the ratio of the sides the same.


Scale factors

A scale factor 'scales up' the ratio of the sides to one another, resulting in similar shapes.

​

Definitions

Scale factor

​When enlarging a shape, each side is multiplied by the same number. This number is known as the scale factor. ​​​

Similar shape

Shapes whose sides have the same ratio between them when simplified. They share the scale factor as a factor.


Working out lengths using a scale factor

Missing lengths can be worked out using a scale factor. 


Example 1

The triangle below has sides of lengths 5cm,7cm5cm, 7cm5cm,7cm and 10cm10cm10cm. What would the lengths be if this triangle was enlarged by a scale factor of two? Write your answer as a ratio.

Maths; Ratio and proportion; KS2 Year 6; Scale factor problems

Multiply each side by two.

5cm×2=10cm7cm×2=14cm10cm×2=20cm5cm \times 2 = {10cm} \\7cm \times 2 = {14cm} \\10cm \times 2 = {20cm}5cm×2=10cm7cm×2=14cm10cm×2=20cm


Write the lengths as a ratio.

10cm:14cm:20cm‾\underline{10cm:14cm:20cm}10cm:14cm:20cm​​​

​

Working out the scale factor using lengths

You might also be asked to work out the scale factor. To do this, divide the end length by the starting length.


Note: Make sure that you are using the same side on each shape when picking your start and end length!


Example 2

A triangle has been enlarged. In terms of ratio, its sides have gone from 3cm:6cm:5cm3cm:6cm:5cm3cm:6cm:5cm to 12cm:24cm:20cm12cm:24cm:20cm12cm:24cm:20cm. Work out the scale factor.


Pick a length and divide the final length by the start length.

12cm÷3cm=4cm12cm\div3cm = 4cm12cm÷3cm=4cm


Remove the units.

The scale factor is 4‾\underline44​.


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Learn with Basics

Learn the basics with theory units and practise what you learned with exercise sets!
Length:
Scaling by simple fractions

Unit 1

Scaling by simple fractions

Multiplication scaling problems

Unit 2

Multiplication scaling problems

Jump Ahead

Score 80% to jump directly to the final unit.

Optional

Scale factor problems

Unit 3

Scale factor problems

Final Test

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FAQs - Frequently Asked Questions

How do I work out the scale factor between two shapes?

To work out the scale factor between two shapes, divide the final length by the starting length.

What are similar shapes?

Similar shapes are those whose sides have the same ratio between them when simplified. They share the scale factor as a factor.

What is a scale factor?

​When enlarging a shape, each side is multiplied by the same number. This number is known as the scale factor.

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