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 In a right-angled triangle, which side is the longest?
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The hypotenuse.
2 What is 92 ?
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81.
3 What is √64 ?
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8, because 8 × 8 = 64.
Level 2 · Core
4 A triangle has legs 5 and 12. What is the area of the square built on the leg of 12?
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144.
5 Legs are 6 and 8. Add the areas of the two squares built on them.
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36 + 64 = 100. That is the square on the hypotenuse, so the hypotenuse is 10.
6 What is 132 ?
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169.
Level 3 · Challenge
7 Legs are 9 and 12. What is the largest whole number the hypotenuse could sensibly be less than?
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Less than 9 + 12 = 21 (and more than 12). The actual answer is 15.
8 √200 lies between which two whole numbers? Write the smaller one.
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196 < 200 < 225, so √200 is between 14 and 15.
9 A triangle has its right angle at the top-right corner. Is the hypotenuse the side that touches that corner, or the one opposite it? (write: opposite)
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The one opposite the right angle — rotation never changes that rule.