Grade 7–9Curriculum · Maths: algebra
Pythagorean Theorem Worksheets — Free with Answers
Practise a² + b² = c² with new right triangles every time: hypotenuse, missing legs and real-life word problems.
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Topics on this worksheet
Areas on this sheet
- Geometry · 20Pythagoras' theorem, circles, volume, distance and scale.
Pythagorean theorem · 14-16 years
Name: ____________________2.A ladder leans against a wall. The foot of the ladder is 14 m from the wall and it reaches 48 m up the wall. How long is the ladder?
4.A 25 m long ramp rises to a height of 7 m. How far is it along the ground?
6.Facts: A 17 m long ramp rises to a height of 8 m. Question: How far is it along the ground?
8.A ladder leans against a wall. The foot of the ladder is 3 m from the wall and it reaches 4 m up the wall. How long is the ladder? Answer with the correct unit.
10.A 34 m long ramp rises to a height of 16 m. How far is it along the ground? Answer with the correct unit.
12.A rectangular field is 10 m long and 13 m wide. Noa walks straight across it diagonally. How long is the walk?
14.A rectangular field is 10 m long and 5 m wide. Robin walks straight across it diagonally. How long is the walk? Answer with the correct unit.
16.Facts: A 5 m long ramp rises to a height of 3 m. Question: How far is it along the ground? Answer with the correct unit.
18.A 10 m long ramp rises to a height of 6 m. How far is it along the ground? Answer with the correct unit.
20.A ladder leans against a wall. The foot of the ladder is 6 m from the wall and it reaches 6 m up the wall. How long is the ladder?
Answer key
- 1. 10 cm
- 2. 50 m
- 3. 15 cm
- 4. 24 m
- 5. ≈ 6.4 cm
- 6. 15 m
- 7. 8 cm
- 8. 5 m
- 9. 25 cm
- 10. 30 m
- 11. 16 cm
- 12. ≈ 16.4 m
- 13. ≈ 9.8 cm
- 14. ≈ 11.2 m
- 15. 48 cm
- 16. 4 m
- 17. 20 cm
- 18. 8 m
- 19. ≈ 13.6 cm
- 20. ≈ 8.5 m
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- Choose the exercise type Pythagorean theorem.
- Pick age group 12–14 or 14–16, difficulty and calculations, word problems or a mix.
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About this generator
The Pythagorean theorem links the three sides of a right triangle. The easier level uses whole-number triples such as 3–4–5 and 5–12–13 so pupils can focus on the method. Harder levels mix in missing legs and answers rounded to one decimal. Word problems cover ladders against walls, ramps and walking diagonally across a field, and the generator also offers distance between two points in a coordinate system. The answer key is calculated by the website, so it always matches the tasks. No sign-up is needed and no personal data is collected.
Popular uses
- First lessons on right triangles
- Ladder, ramp and diagonal problems
- Revision before a test
- Distance in the coordinate system
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Frequently asked questions
- What is the Pythagorean theorem?
- In a right triangle the legs a and b and the hypotenuse c satisfy a² + b² = c².
- How do I find a missing leg?
- Subtract: b² = c² − a², then take the square root.