Pythagoras' theorem: Class 7 practice
In a right-angled triangle, the square on the hypotenuse equals the sum of the squares on the other two sides: c² = a² + b². Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Squares and square roots
The idea behind pythagoras' theorem
In a right-angled triangle, the square on the hypotenuse equals the sum of the squares on the other two sides: c² = a² + b². It only works for right triangles, and the hypotenuse is always opposite the right angle.
Step-by-step method
- Identify the hypotenuse.
- To find c: c = √(a² + b²).
- To find a leg: a = √(c² − b²).
- Check the longest side is the hypotenuse.
Worked example 1 (Basic)
A right triangle has legs 9 cm and 12 cm. Find the hypotenuse.
- c² = 81 + 144 = 225
- c = 15 cm
- Answer: 15 cm
Worked example 2 (Standard)
A right triangle has hypotenuse 39 cm and one leg 15 cm. Find the other leg.
- b² = 1521 − 225 = 1296
- b = 36 cm
- Answer: 36 cm
Worked example 3 (Challenge)
A 25 m ladder leans against a wall with its foot 7 m from the wall. How high up the wall does it reach?
- h² = 25² − 7² = 576
- h = 24 m
- Answer: 24 m
Common mistakes and misconceptions
- Adding when finding a leg
- Using it in non-right triangles
Practice questions
- (Basic) A right triangle has legs 16 cm and 30 cm. Find the hypotenuse.
- (Basic) A right triangle has legs 24 cm and 45 cm. Find the hypotenuse.
- (Standard) A right triangle has hypotenuse 75 cm and one leg 21 cm. Find the other leg.
- (Standard) A right triangle has hypotenuse 34 cm and one leg 16 cm. Find the other leg.
- (Challenge) A 34 m ladder leans against a wall with its foot 16 m from the wall. How high up the wall does it reach?
- (Challenge) A 82 m ladder leans against a wall with its foot 18 m from the wall. How high up the wall does it reach?
Answer key with full working
- Q1: c² = 256 + 900 = 1156 → c = 34 cm → Answer: 34 cm
- Q2: c² = 576 + 2025 = 2601 → c = 51 cm → Answer: 51 cm
- Q3: b² = 5625 − 441 = 5184 → b = 72 cm → Answer: 72 cm
- Q4: b² = 1156 − 256 = 900 → b = 30 cm → Answer: 30 cm
- Q5: h² = 34² − 16² = 900 → h = 30 m → Answer: 30 m
- Q6: h² = 82² − 18² = 6400 → h = 80 m → Answer: 80 m
Syllabus note
This skill is listed under "The Triangle and its Properties" for Class 7 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.
Related practice and notes
Frequently asked questions
Which chapter is pythagoras' theorem in?
"The Triangle and its Properties", Class 7 Maths (NCERT/CBSE). Other boards may place it differently.
How were the answers checked?
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.