Calculating The Shorter Side Lengths in Right Angled Triangles Using Pythagoras’s Theorem

Pythagoras’s Theorem can also be used to work out the length of one of the shorter side lengths. You can do this without the need of any algebra if you follow the 3 steps below.

1) First of all work out the squares of the 2 side lengths that are shown.

2) Work out the difference between the answers from step 1.

3) Square root (√) your answer from step 2.

Note. If you are finding the hypotenuse then you will sum the squares, but all the example shown below will be calculating the length of the shorter sides.

Example 1

Work out the length of side m using Pythagoras.

1) First of all work out the squares of the 2 side lengths that are shown.

10² = 100

9² = 81

2) Work out the difference between the answers from step 1.

100 – 81 = 19

3) √19 = 4.4 cm to 1 decimal place.

Example 2

Work out the length of side n using Pythagoras.

In this example, we are not finding the shortest side, but we still use the same method as above as it’s the second shortest side.

1) First of all work out the squares of the 2 side lengths that are shown.

9.6² = 92.16

2.4² = 5.76

2) Work out the difference between the answers from step 1.

92.16 – 5.76 = 86.4

3) √86.4 = 9.3 cm to 1 decimal place.

Extra links:

Working out the longest side length (hypotenuse) using Pythagoras’s Theorem.

Mixed questions using Pythagoras.

For some harder questions on Pythagoras Theorem click here.