# Enlarging and reducing shapes

A scale factor can be used to enlarge or reduce a shape.

Shape A below is enlarged by scale factor $$2$$ to give Shape B.

### Linear Scale Factor

The scale factor describes the size of an enlargement or reduction.

For example, a scale factor of $$2$$ means that the new shape is twice the size of the original.

A scale factor of $$3$$ means that the new shape is three times the size of the original.

A scale factor of $$\frac{1}{2}$$ means that the new shape is half the size of the original.

To calculate the scale factor, we use the following:

$SF_{Enlargement}=\frac{Big}{Small}$

$SF_{Reduction}=\frac{Small}{Big}$

You can get the 'big' and 'small' from the corresponding sides on the figures.

Question

Rectangles $$PQRS$$ is an enlargement of rectangle $$pqrs$$. What is the length of $$PS$$?

$$PS$$ is on the bigger rectangle, therefore we will be using an enlargement scale factor.

$SF_{Enlargement}= \frac{Big}{Small}=\frac{7}{4}$

Therefore $$PS$$ is $$\frac{7}{4}$$ times $$ps$$.

So, $$PS = \frac{7}{4} \times 9 = 15.75cm$$

(You can type in your calculator $$7 \div 4 \times 9$$)