GCSE MATHS PRACTICE

GCSE Pythagoras Questions

Pythagoras’ theorem applies to right-angled triangles: a² + b² = c², where c is the hypotenuse, the longest side opposite the right angle. Add the squares to find the hypotenuse; subtract a shorter side’s square from the hypotenuse’s square to find the other shorter side. Take the square root to find the length.

Updated 8 October 2026

Worked example

A right-angled triangle has shorter sides of 9 cm and 12 cm. Find its hypotenuse, c.

c is the hypotenuse. Use the given lengths, not measurements from the diagram.

The hypotenuse is opposite the right angle. Use c² = 9² + 12².
c² = 81 + 144 = 225.
Take the positive square root: c = √225 = 15.

Answer: 15 cm

Practice questions

1
Triangle ABC has a right angle at B. Which side is the hypotenuse?
2
A right-angled triangle has shorter sides of 12 cm and 16 cm. Find the hypotenuse.
3
A right-angled triangle has hypotenuse 25 cm and one shorter side 15 cm. Find the other shorter side.
4
A rectangular garden is 7 m long and 11 m wide. Find the length of its diagonal, correct to 1 decimal place.

Show answers

1. AC
2. 20 cm
3. 20 cm
4. 13.0 m

Common mistakes

Using the theorem without a right angle — It applies only to right-angled triangles.
Always adding — Subtract squares when finding a shorter side.
Forgetting the square root — The sum or difference gives a squared length, not the final length.

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GCSE MATHS PRACTICE

GCSE Pythagoras Questions

Updated 8 October 2026

Worked example

A right-angled triangle has shorter sides of 9 cm and 12 cm. Find its hypotenuse, c.

c is the hypotenuse. Use the given lengths, not measurements from the diagram.

The hypotenuse is opposite the right angle. Use c² = 9² + 12².
c² = 81 + 144 = 225.
Take the positive square root: c = √225 = 15.

Answer: 15 cm

Practice questions

1
Triangle ABC has a right angle at B. Which side is the hypotenuse?
2
A right-angled triangle has shorter sides of 12 cm and 16 cm. Find the hypotenuse.
3
A right-angled triangle has hypotenuse 25 cm and one shorter side 15 cm. Find the other shorter side.
4
A rectangular garden is 7 m long and 11 m wide. Find the length of its diagonal, correct to 1 decimal place.

Show answers

1. AC
2. 20 cm
3. 20 cm
4. 13.0 m

Common mistakes

Using the theorem without a right angle — It applies only to right-angled triangles.
Always adding — Subtract squares when finding a shorter side.
Forgetting the square root — The sum or difference gives a squared length, not the final length.

GCSE Pythagoras Questions

Worked example

Enlarged diagram

Practice questions

Common mistakes

GCSE Pythagoras Questions

Worked example

Enlarged diagram

Practice questions

Common mistakes

GCSE Pythagoras Questions

Worked example

Practice questions

Common mistakes

Related resources

GCSE Pythagoras Questions

Worked example

Practice questions

Common mistakes

Related resources