Find Scale Factors and Missing Lengths Using Ratios

In this activity, we will be looking at similar shapes.

Similar shapes have matching corresponding angles and corresponding sides which are in the same ratio.

In these two triangles, the angles match.

The first triangle has sides which are double the length of the sides of the second triangle.

The ratio of the bases is 4 : 2 which simplifies like a fraction to 2 : 1

The ratio of the heights is 8 : 4, which simplifies like a fraction to 2 : 1

Let's look at a typical question!

Example

The rectangles below are similar.

Find the missing length.

Answer

The ratio of the bases is 1:3

This means the sides of the large rectangle are 3 times longer than the small rectangle (1 : 3)   

To find the missing side we know it is 3 times longer than its corresponding side (3)

The missing side = 3 x 3  = 9

Let's have a go at the questions now.