Work through the levels in order. Type your answer and press Check — open the worked solution if you get stuck. Answers like -6, 3/4 or 0.25 are typed exactly as shown.
Level 1 · Warm-up
1 Legs are 3 and 4. Find the hypotenuse.
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c = √25 = 5.
2 Legs are 6 and 8. Find the hypotenuse.
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c = 10.
3 Legs are 8 and 15. Find the hypotenuse.
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c = √289 = 17.
Level 2 · Core
4 A rectangle is 9 cm by 12 cm. Find the length of its diagonal. (cm)
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81 + 144 = 225 → d = 15 cm.
5 A ladder's foot is 1.4 m from a wall and it reaches 4.8 m up. How long is the ladder? (m)
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1.96 + 23.04 = 25 → 5 m.
6 Legs are 5 and 9. Find c to 2 decimal places.
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√106 = 10.30 (2 d.p.).
Level 3 · Challenge
7 Someone walks 300 m east then 400 m north. How far are they from the start? (m)
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90000 + 160,000 = 250,000 → 500 m.
8 A right-angled triangle has legs 5 and 12. Find its PERIMETER.
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c = 13, so P = 5 + 12 + 13 = 30.
9 Legs are 7 and 11. Find c to 2 decimal places.
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√170 = 13.04 (2 d.p.). Sense-check: between 13 and 14 ✓