Geometry and proof · Ages 13–14

Finding the hypotenuse worksheet

Part of: Pythagoras' theorem

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Geometry and proof · Ages 13–14

Numsprite
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Write each answer in the space. For word problems, show your working and write a sentence answer.

1.In the right-angled triangle, how long is the hypotenuse ?, in cm?
Answer:
2.A right-angled triangle's legs are 36 cm and 15 cm: 36² + 15² = + = , so the hypotenuse = cm.
Fill in each blank
Answer:
3.A right-angled triangle has legs of 7 cm and 6 cm. How long is its hypotenuse, in cm, to 1 decimal place?
Answer:
4.In the right-angled triangle, the hypotenuse ? = cm.
Answer:
5.A right-angled triangle has legs of 2 cm and 2 cm. How long is its hypotenuse, in cm, to 1 decimal place?
Answer:
6.A right-angled triangle's legs are 17 cm and 6 cm. The hypotenuse = cm.
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7.A right-angled triangle's legs are 1.2 m and 50 cm. How long is its hypotenuse, in cm?
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8.A right-angled triangle's legs are 0.6 m and 0.8 m. How long is its hypotenuse, in m?
Answer:

9.Triangle ABC in the picture is right-angled. Which side is the hypotenuse?
- A. CA
- B. AB
- C. BC
- D. It has none
Choose the right answer
Answer:
10.A right-angled triangle with legs of 24 cm and 32 cm has a hypotenuse of 41 cm.
True or false?
Answer:
11.The right-angled triangle's legs are 6 cm and 8 cm. How long is its hypotenuse, in cm?
- A. 100
- B. 10
- C. 24
- D. 14
Choose the right answer
Answer:
12.A right-angled triangle with legs of 27 cm and 120 cm has a hypotenuse of 124 cm.
True or false?
Answer:

13.Ka-yee walks 21 m east from home, then 64 m north to the park. About how far is the park from home in a straight line, in m, to 1 decimal place?
Working:
Answer:
14.A flagpole is 5 m tall. A rope runs straight from its top to a point on the ground 7 m from its foot. About how long is the rope, in m, to 1 decimal place?
Working:
Answer:
15.A boat sails 18 km east from the pier, then 80 km north. 18² + 80² = , so the boat is km from the pier.
Fill in each blank
Working:
Answer:
16.A right-angled triangular flower bed has legs of 40 m and 9 m, and a fence goes all round it. The hypotenuse is m, and the fence m in all.
Fill in each blank
Working:
Answer:
17.In right-angled triangle ABC, ∠B = 90°, AB = 9 cm and BC = 12 cm. Using the hypotenuse AC as a leg, right-angled triangle ACD is drawn with ∠ACD = 90° and CD = 8 cm. How long is AD, in cm?
Working:
Answer:
18.A rectangular photo frame is 27 cm wide and 120 cm high. Find the length d of its diagonal: put the steps in order.
- A. d = 15129 = 123
- B. = 15129
- C. d² = 27² + 120²
- D. = 729 + 14400
Write the letters in the right order
Working:
Answer:

Show the answers and working

Finding the hypotenuse worksheet: Answers and working

1. 13 cm
12² + 5² = 144 + 25 = 169, so the hypotenuse = 169 = 13 cm.
2. 1296, 225, 1521, 39
Square each first, 1296 and 225, which add to 1521; 1521 = 39 × 39, so the hypotenuse is 39 cm.
3. 9.2 cm
7² + 6² = 85, so the hypotenuse = 85 ≈ 9.2 cm.
4. 106
9² + 5² = 81 + 25 = 106, not a square number, so the root doesn't come out whole: the hypotenuse is 106 cm.
5. 2.8 cm
2² + 2² = 8, so the hypotenuse = 8 ≈ 2.8 cm.
6. 53
(17)² = 17, with no more squaring to do: 17 + 6² = 17 + 36 = 53, so the hypotenuse = 53 cm.
7. 130 cm
Put both in one unit first: 1.2 m = 120 cm. 120² + 50² = 14400 + 2500 = 16900, so the hypotenuse = 16900 = 130 cm.
8. 1 m
0.6² + 0.8² = 0.36 + 0.64 = 1, so the hypotenuse = 1 = 1 m.

9. B. AB
Find the right angle (the one with the little square); the side facing it, not touching that corner, is the hypotenuse, the longest side.
10. False
24² + 32² = 576 + 1024 = 1600, so the hypotenuse = 1600 = 40 cm.
11. B. 10
6² + 8² = 100, so the hypotenuse = 100 = 10 cm.
12. False
27² + 120² = 729 + 14400 = 15129, so the hypotenuse = 15129 = 123 cm.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. 67.4 m
East and north meet at a right angle: the straight distance = 21² + 64² = 4537 ≈ 67.4 m.
14. 8.6 m
The pole stands at right angles to the ground and the rope is the hypotenuse: 5² + 7² = 74, so the rope = 74 ≈ 8.6 m.
15. 6724, 82
East and north meet at a right angle, so the distance back is the hypotenuse: 324 + 6400 = 6724, 6724 = 82 km.
16. 41, 90
The hypotenuse = 40² + 9² = 1681 = 41 m; the fence = 40 + 9 + 41 = 90 m.
17. 17 cm
First the shared side: AC = 9² + 12² = 15 cm; then AD = 15² + 8² = 17 cm.
18. C → D → B → A
The diagonal is the hypotenuse of the right triangle the sides make: square, add, then the root, d = 123 cm.

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