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Solve Problems Using Pythagoras' Theorem

In this worksheet, students will apply Pythagoras' theorem to solve simple problems.

'Solve Problems Using Pythagoras' Theorem' worksheet

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR,

Curriculum topic:   Geometry and Measures, Mensuration

Curriculum subtopic:   Mensuration and Calculation Triangle Mensuration

Difficulty level:  

Worksheet Overview

We already know that Pythagoras was a top bloke.

He did come up with the theorem on how to work out the length of sides for triangles after all.


wooly hat


Let us put our thinking cap on the revise the theorem


Remember this theorem only works for right-angled triangles.


To find the hypotenuse (longer side) of a triangle:


right angles triangle without hypotenuse length


10² + 3² =  √109 = 10.44 cm to 2 decimal places



To find the shorter side length:


right angled triangle with shorter side length missing


9² - 7² =√32 = 5.66 to 2 decimal places


The key point here is to remember when to add and when to subtract.

Now, we are okay with using Pythagoras' theorem, we can apply this to solve all sorts of problems.


sketch book




I leave my house to go to the bus stop.

I walk 20 m due west and then walk another 30 m due north.

If I had taken the direct route how far would I have walked?


   30 M___________ 

              20 M


Here you can see a right-angled triangle has been formed.

The direct route would be the diagonal (hypotenuse)


20² + 30² = √1300 = 36.05 m



You are always looking to sketch the situation out or turn a diagram into a right angles triangle.

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