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Ratio and proportion

Scale factor problems

Scale factor problems

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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.


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, 7cm and 10cm10cm. 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}

Write the lengths as a ratio.


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:5cm to 12cm: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 = 4cm

Remove the units.

The scale factor is 4\underline4.

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FAQs - Frequently Asked Questions

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

What are similar shapes?

What is a scale factor?


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