Similar Lengths

Exam code: 4024

Written by: Ashika|Reviewed by: Caroline Carroll|Updated 2 July 2026

Similar Lengthsvideo

Similar Lengths

Similar lengths

How do I find the scale factor between lengths on similar shapes?

Equivalent lengths on two similar shapes will be in the same ratio and are linked by a scale factor
Establish the type of enlargement
- If the second shape is bigger
  - then the scale factor is greater than 1
- If the second shape is smaller
  - then the scale factor is greater than 0 but less than 1
To find the scale factor
- Identify known lengths of corresponding sides
- Divide the length on the second shape by the corresponding length on the first shape

How do I find missing lengths on similar shapes?

Method 1

STEP 1
Find the scale factor to get from the first shape to the second shape
- Divide a length on the second by the corresponding length on the first
- The scale factor can be less than 1 for this method
STEP 2
Use the scale factor to find the length you need
- To find a missing length on the second shape
  - Multiply the corresponding length on the first shape by the scale factor
- To find a missing length on the first shape
  - Divide the corresponding length on the first shape by the scale factor

Method 2

STEP 1
Find the scale factor to get from the smaller shape to the bigger shape
- Divide a length on the bigger shape by the corresponding length on the smaller shape
- The scale factor is always greater than 1 for this method
STEP 2
Use the scale factor to find the length you need
- To find a missing length on the bigger shape
  - Multiply the corresponding length on the smaller shape by the scale factor
- To find a missing length on the smaller shape
  - Divide the corresponding length on the bigger shape by the scale factor

Worked example

ABCD and PQRS are similar shapes.
Find the length of PS.

Answer:

The two shapes are mathematically similar

Identify two known corresponding sides of the similar shapes

AB and PQ are corresponding sides

Method 1

The second shape is smaller than the first shape so the scale factor will be between 0 and 1
Divide the known length on the second shape by the corresponding length on the first shape to find the scale factor

$\begin{array}{rcl} Scale Factor & = & \frac{3}{6} = \frac{1}{2} \end{array}$

Multiply the length AD by the scale factor to find its corresponding length PS on the second shape

$\begin{array}{rcl} P S & = & \frac{1}{2} \times 15 = \frac{15}{2} \end{array}$

$P S = 7.5 cm$

Method 2

Divide the known length on the bigger shape by the corresponding length on the smaller shape to find the scale factor

$\begin{array}{rcl} Scale Factor & = & \frac{6}{3} = 2 \end{array}$

The missing length is on the smaller shape

Divide the length AD by the scale factor to find its corresponding length PS on the smaller shape

$P S = 15 \div 2$