The Pythagorean theorem
Grades 8 to 10 (Years 8 to 11 in England) · 16 questions · Common Core: 8.G.B.6, 8.G.B.7 · England: GCSE Foundation Geometry, GCSE Higher Geometry, KS3 Geometry and measures
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Score/ 16
Question 1
A box is 6 cm by 9 cm by 18 cm. What is the length of the longest straight rod that fits inside, from one corner to the opposite corner, in cm?
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Question 2
A right triangle has hypotenuse 16 cm and one leg 12 cm. Find the other leg, to 1 decimal place.
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Question 3
A rectangular park is 52 m long and 49 m wide. Instead of walking along two sides, you cut across the diagonal. How many metres shorter is the shortcut? Round to the nearest metre.
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Question 4
A right triangle has legs 21 m and 72 m. How long is the hypotenuse, in m?
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Question 5
The legs of a right triangle are 6 cm and 8 cm. Find the hypotenuse, to 1 decimal place.
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Question 6
A right triangle has hypotenuse 26 yd and one leg 10 yd. How long is the other leg, in yd?
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Question 7
A triangle has sides 7, 24 and 27. Is it a right triangle?
- A. Yes
- B. No
Question 8
A ladder leans against a wall. Its foot is 9 m from the wall and it reaches 5 m up the wall. How long is the ladder? Round to 1 decimal place.
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Question 9
Tariq says the hypotenuse of a right triangle with legs 8 and 15 is 23, because you add the legs. What is it really?
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Question 10
Kwame builds a garden frame with sides 10 dm and 24 dm and wants a perfect right-angled corner. How long should the diagonal brace be, in dm?
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Question 11
A right triangle has legs 9 m and 12 m. How long is the hypotenuse, in m?
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Question 12
A 13 m ladder leans against a wall. Its foot is 5 m from the wall. How high up the wall does it reach, in m?
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Question 13
A right triangle has hypotenuse 5 m and one leg 4 m. How long is the other leg, in m?
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Question 14
A box is 4 cm by 12 cm by 18 cm. What is the length of the longest straight rod that fits inside, from one corner to the opposite corner, in cm?
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Question 15
A right triangle has hypotenuse 17 cm and one leg 3 cm. Find the other leg, to 1 decimal place.
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Question 16
A rectangular park is 41 m long and 37 m wide. Instead of walking along two sides, you cut across the diagonal. How many metres shorter is the shortcut? Round to the nearest metre.
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