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. A ⭐ Bonus Challenge at the end is extra credit — skip it if the rest was hard work.
Level 1 · Warm-up
1 In Pythagoras' theorem a2 + b2 = c2, which side is c?
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The hypotenuse.
2 Legs are 3 and 4. What is c2 ?
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25, so c = 5.
3 You find c2 = 100. What is c?
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10.
Level 2 · Core
4 Legs are 6 and 8. Find c.
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c = √100 = 10.
5 Legs are 5 and 12. Find c.
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c = √169 = 13.
6 Is a triangle with sides 8, 15, 17 right-angled?
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64 + 225 = 289 and 172 = 289, so yes.
Level 3 · Challenge
7 Is a triangle with sides 5, 6, 8 right-angled?
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61 ≠ 64, so no.
8 Legs are 5 and 7. Find c2.
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74, so c = √74 ≈ 8.60.
9 Legs are 4 and 9. Find c to 2 decimal places.
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√97 = 9.85 (2 d.p.). Sense-check: between 9 and 10 ✓