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.

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Definitions

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

Multiply each side by two.

$$5cm \times 2 = {10cm} \\7cm \times 2 = {14cm} \\10cm \times 2 = {20cm}$$

Write the lengths as a ratio.

$$\underline{10cm:14cm:20cm}$$​​

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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 $$3cm:6cm:5cm$$ to $$12cm:24cm:20cm$$. Work out the scale factor.

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

$$12cm\div3cm = 4cm$$

Remove the units.

The scale factor is $$\underline4$$.