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Pythagoras practice questions with answers

Foundation and Higher · Grade 4

A second set of Pythagoras questions for GCSE Maths. They are different from the ones on the topic page, so work through both. Try each question, then open the answer to check your working.

More questions

Question 1 Easy

Find the distance between the coordinates (1, 2) and (9, 17).

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Answer: 17

  1. The gaps are 8 and 15.
  2. 8² + 15² = 289.
  • Method (1): The gaps are 8 and 15.
  • Accuracy (1): Answer 17

Question 2 Easy

A triangle has sides 6 cm, 8 cm and 10 cm. Is it right-angled? Answer yes or no.

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Answer: yes

  1. 6² + 8² = 10².
  2. The triangle is right-angled.
  • Method (1): 6² + 8² = 10².
  • Accuracy (1): Answer yes

Question 3 Medium

A square has a diagonal of 10 cm. Find the side length as a surd.

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Answer: 5√2

  1. Half of 10² is 50.
  2. The side is 5√2.
  • Method (1): Half of 10² is 50.
  • Accuracy (1): Answer 5√2

Question 4 Medium

A right-angled triangle has shorter sides 6 cm and 8 cm. Give the hypotenuse and the perimeter, hypotenuse first.

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Answer: 10, 24

  1. The hypotenuse is 10 cm.
  2. The perimeter is 6 + 8 + 10 = 24 cm.
  • Method (1): The hypotenuse is 10 cm.
  • Accuracy (1): Answer 10, 24

Question 5 Hard

A cuboid has edges 2 cm, 3 cm and 6 cm. What is the length of the space diagonal?

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Answer: 7

  1. 2² + 3² + 6² = 49.
  2. The space diagonal is 7.
  • Method (1): 2² + 3² + 6² = 49.
  • Accuracy (1): Answer 7

Question 6 Hard

The hypotenuse is the diameter of a circle. The shorter sides are 7 cm and 24 cm. What is the radius?

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Answer: 12.5

  1. The hypotenuse is 25 cm, and that is the diameter.
  2. The radius is 12.5 cm.
  • Method (1): The hypotenuse is 25 cm, and that is the diameter.
  • Accuracy (1): Answer 12.5

Exam-style question

A longer question with marks, in the style of a written paper. This is a Yumio practice question, not a past paper question.

Exam-style question 13 marks

The distance from (0, 0) to (8, y) is 17. Find the missing positive coordinate y.

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Answer: 15

  1. 17² − 8² = 225.
  2. The positive coordinate is 15.
  • Method (1): 17² − 8² = 225.
  • Method (1): The positive coordinate is 15.
  • Accuracy (1): Answer 15

Quick checks

Short one-step questions. Pick an option before you open the answer.

Check 1

A ladder 29 m long leans against a vertical wall. The foot of the ladder is 20 m from the wall. How high up the wall does the ladder reach?

  1. 21
  2. 35.2
  3. 441
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21 The result is 21.

Check 2

A triangle has sides of 7 cm, 24 cm and 28 cm. Is the triangle right-angled? Answer yes or no.

  1. No
  2. Yes
  3. Not enough information
Show answer

No The result is No.

Check 3

A right-angled triangle has shorter sides 3 cm and 8 cm. Work out the length of the hypotenuse. Give your answer to 1 decimal place.

  1. 8.5
  2. 11
  3. 73
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8.5 The result is 8.5.

Check 4

In triangle ABC, angle B is 90°, AB = 8 cm and BC = 15 cm. Work out the length of AC.

  1. 17
  2. 23
  3. 289
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17 The result is 17.

Check 5

In triangle PQR, angle Q is 90°, PR = 30 cm and QR = 18 cm. Work out the length of PQ.

  1. 24
  2. 35
  3. 576
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24 The result is 24.

Check 6

A rectangle is 15 cm long and 36 cm wide. Work out the length of its diagonal.

  1. 39
  2. 51
  3. 1521
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39 The result is 39.

Check 7

A point is 12 cm across and 16 cm up from the origin O. How far is the point from O?

  1. 20
  2. 28
  3. 400
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20 The result is 20.

Check 8

The diagonal of a rectangle is 5 cm and one side is 3 cm. Work out the length of the other side.

  1. 4
  2. 5.8
  3. 16
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4 The result is 4.

Check 9

A wire is fixed to the top of a vertical pole that is 16 m tall. The other end is fixed to the ground 12 m from the base of the pole. How long is the wire?

  1. 20
  2. 28
  3. 400
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20 The result is 20.

Check 10

A right-angled triangle has shorter sides 9 and 12. How long is the hypotenuse?

  1. 15
  2. 21
  3. 225
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15 The result is 15.

Check 11

A right-angled triangle has hypotenuse 25 and one shorter side 7. How long is the other shorter side?

  1. 24
  2. 26
  3. 576
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24 The result is 24.

Check 12

A ladder 29 m long leans against a vertical wall. The foot of the ladder is 20 m from the wall. How high up the wall does the ladder reach?

  1. 21
  2. 35.2
  3. 441
Show answer

21 The result is 21.

Check 13

A triangle has sides of 8 cm, 15 cm and 19 cm. Is the triangle right-angled? Answer yes or no.

  1. No
  2. Yes
  3. Not enough information
Show answer

No The result is No.

Check 14

A right-angled triangle has shorter sides 2 cm and 7 cm. Work out the length of the hypotenuse. Give your answer to 1 decimal place.

  1. 7.3
  2. 9
  3. 53
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7.3 The result is 7.3.

Check 15

In triangle ABC, angle B is 90°, AB = 5 cm and BC = 12 cm. Work out the length of AC.

  1. 13
  2. 17
  3. 169
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13 The result is 13.

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