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Edexcel IGCSE Maths (4MA1) · Unit 5: Geometry

IGCSE Maths Pythagoras' Theorem Questions and Answers

Pythagoras' Theorem questions with full solutions for Pearson Edexcel International GCSE Mathematics A (4MA1), Higher tier. Read the 3 worked examples first, then cover each solution and redo it yourself.

Practise Pythagoras' theorem in Unit 5 →Pythagoras' Theorem revision notes

What this topic covers

Pythagoras' Theorem worked examples

Worked example 1: Finding the hypotenuse

Find the hypotenuse of a right-angled triangle with shorter sides 8 cm and 15 cm.

Solution

  1. \(c^2=8^2+15^2=289\).
  2. \(c=17\) cm.

Answer: 17 cm

Tip: The hypotenuse is opposite the right angle.

Worked example 2: Ladder problem

A 6.5 m ladder leans against a wall with its foot 2.5 m from the wall. How high up the wall does it reach?

Solution

  1. The ladder is the hypotenuse: \(h^2=6.5^2-2.5^2=36\).
  2. \(h=6\) m.

Answer: 6 m

Tip: For a shorter side, subtract.

Worked example 3: Pythagoras in 3D

Find the length of the space diagonal of a 3 cm × 4 cm × 12 cm cuboid.

Solution

  1. \(d^2=3^2+4^2+12^2=169\).
  2. \(d=13\) cm.

Answer: 13 cm

Tip: Or find the base diagonal (5 cm) first.

Every question and worked example here is original, written for IGCSE Math Revision rather than copied from Pearson papers, and each answer was re-solved independently before publishing.

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Questions students ask

Which Edexcel IGCSE Maths papers test Pythagoras' theorem?

Either Higher tier paper, 1H or 2H, can test Pythagoras' theorem: both cover the whole Pearson Edexcel International GCSE Mathematics A (4MA1) specification and both allow a calculator. Show your method, because most marks are for working.

Where can I practise more Pythagoras' theorem questions?

In the IGCSE student hub: Unit 5 (Geometry) has more exam-style questions on this topic, each with a mark scheme. Practice starts with a 7-day free trial; the worked examples and questions on this page are free.

More Unit 5 topics: Geometry