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
Kofi says the hypotenuse of a right triangle with legs 3 and 4 is 7, because you add the legs. What is it really?
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Question 2
A right triangle has hypotenuse 12 cm and one leg 8 cm. Find the other leg, to 1 decimal place.
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Question 3
A rectangular park is 11 m by 7 m. How long is the diagonal path across it? Round to 1 decimal place.
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Question 4
A 5 m ladder leans against a wall. Its foot is 3 m from the wall. How high up the wall does it reach, in m?
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Question 5
A triangle has sides 3, 4 and 5. Is it a right triangle?
- A. Yes
- B. No
Question 6
A rectangular park is 96 m long and 33 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 7
Kwame builds a garden frame with sides 15 dm and 36 dm and wants a perfect right-angled corner. How long should the diagonal brace be, in dm?
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Question 8
A right triangle has legs 8 m and 15 m. How long is the hypotenuse, in m?
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Question 9
The legs of a right triangle are 4 cm and 2 cm. Find the hypotenuse, to 1 decimal place.
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Question 10
A right triangle has hypotenuse 75 ft and one leg 21 ft. How long is the other leg, in ft?
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Question 11
A box is 6 cm by 18 cm by 27 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 12
A right triangle has hypotenuse 51 m and one leg 45 m. How long is the other leg, in m?
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Question 13
A right triangle has legs 20 ft and 48 ft. How long is the hypotenuse, in ft?
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Question 14
Maya says the hypotenuse of a right triangle with legs 7 and 24 is 31, because you add the legs. What is it really?
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Question 15
A right triangle has hypotenuse 11 cm and one leg 2 cm. Find the other leg, to 1 decimal place.
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Question 16
A ladder leans against a wall. Its foot is 12 m from the wall and it reaches 7 m up the wall. How long is the ladder? Round to 1 decimal place.
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