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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.

### 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 $5cm, 7cm$ 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.

$\underline{10cm:14cm:20cm}$​​

### 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 $\underline4$.

## FAQs - Frequently Asked Questions

### What is a scale factor?

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