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Year 9 Mathematics · Pythagoras' theorem

Name: ______________________

Date: ____________

1. A right-angled triangle has shorter sides of 3 cm and 4 cm. How long is the hypotenuse?
- ☐ (a) 7 cm
- ☐ (b) 5 cm
- ☐ (c) 12 cm
- ☐ (d) 25 cm
2. Which side of a right-angled triangle is the hypotenuse?
- ☐ (a) The side opposite the right angle
- ☐ (b) The shortest side
- ☐ (c) The side at the bottom
- ☐ (d) Either side touching the right angle
3. Which set of side lengths makes a right-angled triangle?
- ☐ (a) 6, 7, 9
- ☐ (b) 5, 10, 12
- ☐ (c) 4, 5, 6
- ☐ (d) 8, 15, 17
4. A right-angled triangle has a hypotenuse of 10 cm and one shorter side of 6 cm. How long is the other side?
- ☐ (a) 4 cm
- ☐ (b) 11.66 cm
- ☐ (c) 8 cm
- ☐ (d) 16 cm
5. A 5 m ladder leans against a vertical wall. Its foot is 3 m from the base of the wall on level ground. How high up the wall does it reach?
- ☐ (a) 2 m
- ☐ (b) 4 m
- ☐ (c) 5.83 m
- ☐ (d) 8 m
6. A right-angled triangle has shorter sides of 9 cm and 12 cm. Find the length of the hypotenuse in cm.
7. A right-angled triangle has a hypotenuse of 26 m and a shorter side of 10 m. Find the other side in metres.
8. A right-angled triangle has shorter sides of 5 cm and 7 cm. Find the hypotenuse in cm, correct to one decimal place.

Answer sheet

1. 5 cm — 3^2 + 4^2 = 9 + 16 = 25, and sqrt(25) = 5 cm.
2. The side opposite the right angle — The hypotenuse is opposite the right angle and is always the longest side, whichever way the triangle is drawn.
3. 8, 15, 17 — 8^2 + 15^2 = 64 + 225 = 289 = 17^2. The other sets fail: 36 + 49 = 85 ≠ 81, 25 + 100 = 125 ≠ 144, 16 + 25 = 41 ≠ 36.
4. 8 cm — 10^2 − 6^2 = 100 − 36 = 64, and sqrt(64) = 8 cm.
5. 4 m — The ladder is the hypotenuse. 5^2 − 3^2 = 25 − 9 = 16, and sqrt(16) = 4 m.
6. 15 cm — 9^2 + 12^2 = 81 + 144 = 225, and sqrt(225) = 15 cm.
7. 24 m — 26^2 − 10^2 = 676 − 100 = 576, and sqrt(576) = 24 m.
8. 8.6 cm — 5^2 + 7^2 = 25 + 49 = 74, and sqrt(74) ≈ 8.602, which rounds to 8.6 cm.