Question 1Warm-upFoundation
The two shorter sides of a right-angled triangle are 6 cm and 8 cm. Find the hypotenuse.
Square, add, square root.
Worked solution
- cm
Answer: cm
GCSE & IGCSE maths practice
Pythagoras' theorem questions and answers
In a right-angled triangle, , where is the hypotenuse (the longest side, opposite the right angle). To find the hypotenuse, square and add, then square root. To find a shorter side, square and subtract. Check your answer: the hypotenuse must be the longest side.
8 questions · Foundation and Higher tier · Every answer is checked as you type it, with a full worked solution. Updated .
Where pythagoras' theorem comes up
| GCSE (AQA, Edexcel, OCR) | Foundation and Higher: know and apply Pythagoras' theorem to find lengths in right-angled triangles in 2D. Higher only: in 3D figures. |
|---|---|
| Cambridge IGCSE (0580) | Core and Extended: know and use Pythagoras' theorem. Extended: in three dimensions. |
The method
- Label the hypotenuse c (opposite the right angle).
- Hypotenuse: c = √(a² + b²).
- Shorter side: a = √(c² − b²).
- 3D (Higher): use Pythagoras twice, or d = √(a² + b² + c²) for a cuboid's diagonal.
Pythagoras' theorem questions
Try each one before looking at the hint. If you're stuck, the AI tutor can talk you through it step by step.
Warm-up
Question 2Warm-upFoundation
The two shorter sides of a right-angled triangle are 5 cm and 12 cm. Find the hypotenuse.
25 + 144.
Worked solution
- cm
Answer: cm
Exam-style
Question 3Exam-styleFoundation
A right-angled triangle has hypotenuse 17 cm and one side 8 cm. Find the other side.
Square and subtract.
Worked solution
- cm
Answer: cm
Question 4Exam-styleFoundation
The shorter sides are 4 cm and 7 cm. Find the hypotenuse, to 1 decimal place.
16 + 49.
Worked solution
- cm
Answer: cm
Question 5Exam-styleFoundation
The hypotenuse is 10 cm and one side is 6.5 cm. Find the other side, to 1 decimal place.
100 − 42.25.
Worked solution
- cm
Answer: cm
Question 6Exam-styleFoundation
A 5 m ladder leans against a wall. Its foot is 1.5 m from the wall. How high up the wall does it reach, to 3 significant figures?
The ladder is the hypotenuse.
Worked solution
- m
Answer: m
Challenge
Question 7ChallengeFoundation
A triangle has sides 7 cm, 24 cm and 25 cm. Is it right-angled?
Check whether a² + b² = c².
Worked solution
- and ✓
Answer: Yes:
Question 8ChallengeHigher
A cuboid is 3 cm by 4 cm by 12 cm. Find the length of its longest diagonal (corner to opposite corner).
√(a² + b² + c²).
Worked solution
- cm
Answer: cm
Common mistakes
- Adding when finding a shorter side.
- Forgetting the square root.
- Using a side that isn't the hypotenuse as c.
Stuck on one of these?
The TutorAura AI tutor works through it with you step by step, with the reason for each step, then gives you one like it to try. It checks your working too.
Try the AI tutor freeMore maths questions
Trigonometry (SOH CAH TOA) questions
8 questions with answers
Midpoint and length of a line segment questions
8 questions with answers
Area and perimeter questions
8 questions with answers
GCSE maths mock papers · IGCSE maths mock papers · All maths topics
Sources
The questions are our own. The “where it comes up” notes are from each board's published specification, checked on 26 October 2026:
Practise maths with your own AI tutor
Questions at your level, help when you're stuck, and a plan for your exams. Free for 3 days, no card needed.