Mastering Pythagoras' Theorem
Mathematics
GCSE Foundation
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A worksheet covering Pythagoras' Theorem for GCSE Foundation students.
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Mastering Pythagoras' Theorem
Subject: MathematicsGrade: GCSE Foundation
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Untitled Worksheet
Grade GCSE Foundation
A
Introduction
Review the Pythagoras' Theorem: In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides: c² = a² + b².
B
Practice Questions
Answer all questions. Show your working in the grid spaces provided.
1.
Calculate the length of the hypotenuse of a right-angled triangle with sides 3 cm and 4 cm.
[2 marks]2.
Find the length of side b in a right triangle where sides a = 5 cm, hypotenuse c = 13 cm.
[2 marks]3.
A ladder is leaning against a wall, reaching 8 meters high. The base of the ladder is 6 meters from the wall. Calculate the length of the ladder.
[3 marks]4.
In a right-angled triangle, if the hypotenuse is 10 units and one side is 6 units, find the length of the other side.
[3 marks]5.
A square has a diagonal of 14 cm. Find the length of each side.
[3 marks]6.
A right-angled triangle has legs of lengths 9 cm and 12 cm. What is the length of the hypotenuse?
[2 marks]7.
Determine whether a triangle with sides 7 cm, 24 cm, and 25 cm is a right-angled triangle.
[2 marks]8.
A ramp rises 3 meters vertically and has a length of 5 meters. Is it a right-angled triangle? Show your working.
[3 marks]9.
A triangle has sides of 8 cm, 15 cm, and x cm. If the triangle is right-angled, find the value of x.
[3 marks]10.
A real-world scenario: A ladder leans against a building, reaching 9 meters high. The base is 4 meters from the building. How long is the ladder? Show your working.
[3 marks]11.
Challenge: A right-angled triangle has one leg that is twice as long as the other. The hypotenuse is 10 units. Find the lengths of the legs.
[4 marks]Quick Actions
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Details
- Created
- 12/30/2025
- Updated
- 12/30/2025
- Type
- worksheet