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Mathematics · Year 8
Pythagoras' theorem is a rule for right-angled triangles: the two shorter sides (legs), each squared and added together, equal the longest side (the hypotenuse) squared — written a² + b² = c². It's genuinely useful outside the classroom too: it's how builders check a corner is truly square, and how you'd work out the shortest distance across a rectangular space.
Example
A right-angled triangle has legs of 3m and 4m. The hypotenuse is √(3² + 4²) = √(9 + 16) = √25 = 5m. This '3-4-5' triangle is exactly how builders check that a corner is a true right angle.
Key terms
Questions
1. In a right-angled triangle, the longest side is called the:
2. Pythagoras' theorem only works for triangles that have a:
3. 3² =
4. 4² =
5. √25 =
6. √9 =
7. In a triangle with legs 3 and 4, what is 3² + 4²?
8. A right-angled triangle has legs of 3m and 4m. The hypotenuse is:
9. A right-angled triangle has legs of 6cm and 8cm. The hypotenuse is:
10. A right-angled triangle has legs of 5m and 12m. The hypotenuse is:
11. A ladder leans against a wall, its base 3m from the wall and the wall height 4m. How long is the ladder?
12. A right-angled triangle has legs of 9cm and 12cm. The hypotenuse is:
13. A TV screen is 24 inches wide and 18 inches tall. What is its diagonal size (inches)?
14. A right-angled triangle has legs of 8m and 15m. The hypotenuse is:
15. A ladder is 10m long and its base is 6m from the wall. How high up the wall does it reach?
16. A right-angled triangle has a hypotenuse of 13cm and one leg of 5cm. The other leg is:
17. A rectangular gate is 4m wide with a diagonal brace measuring 5m. How tall is the gate?
18. A right-angled triangle has a hypotenuse of 25m and one leg of 7m. The other leg is:
19. A boat sails 6km east then 8km north. How far is it from its starting point in a straight line?
20. To check a corner is square, a builder measures 3m and 4m along the two walls. How long should the diagonal be for a perfect right angle?
21. A right-angled triangle has legs of 20cm and 21cm. The hypotenuse is:
Answer key (parent copy)