Edexcel International GCSE Mathematics A · 4MA1
Pythagoras’ theorem
Pythagoras’ theorem relates the three side lengths of a right-angled triangle. The square of the hypotenuse equals the sum of the squares of the shorter sides. The final length still requires a square root after working with squares.
Key method
Use a² + b² = c², with c the hypotenuse. To find a shorter side, subtract the other shorter side’s square from c².
Worked example
A ladder is 13 m long and its foot is 5 m from a vertical wall. How high does it reach?
- The wall and level ground form a right angle; the ladder is the hypotenuse.
- Write h² = 13² − 5² = 169 − 25 = 144.
- Take the positive square root because height is a length.
Answer and interpretation
12 m.
Common mistake
Adding the squares when finding a shorter side produces a length greater than the hypotenuse.
Practise independently
Find the diagonal of a rectangle with sides 6 cm and 8 cm.
Check your answer
√(6² + 8²) = 10 cm.
Syllabus connection
This lesson develops pythagoras' theorem within the geometry area. Start with the worked method, attempt the independent question without looking at its answer, then explain any correction in your own words. Check the official specification for your tier’s full requirements.
Related resources
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