6.4 Use of Pythagoras’ theorem in 2D and 3D Quiz: AQA Further Maths, Unit 6

The 20 questions

1. In a right-angled triangle, how is hypotenuse c related to shorter sides a and b?

   • c = a² + b²
   • c² = a² - b²
   • c² = (a + b)²
   • c² = a² + b²

2. Which set of numbers is a Pythagorean triple?

   • 4, 5, 6
   • 6, 7, 9
   • 2, 3, 4
   • 5, 12, 13

3. A right-angled triangle has shorter sides 8 cm and 15 cm. What is its hypotenuse?

   • 23 cm
   • 17 cm
   • 13 cm
   • 19 cm

4. Which triple is a simple multiple of 3, 4, 5?

   • 6, 8, 10
   • 9, 12, 14
   • 6, 8, 11
   • 4, 5, 7

5. In the Pythagorean triple 7, 24, 25, which number is the hypotenuse?

   • 25
   • 7
   • 31
   • 24

6. A right-angled triangle has legs 9 cm and 12 cm. What is the length of the hypotenuse?

   • 18 cm
   • 21 cm
   • 15 cm
   • 13 cm

7. What is the hypotenuse of a right-angled triangle with legs 20 cm and 21 cm?

   • 29 cm
   • 41 cm
   • 27 cm
   • 1 cm

8. Which number completes the Pythagorean triple 9, 40, ?

   • 49
   • 41
   • 45
   • 39

9. A rectangle measures 6 cm by 8 cm. What is the length of its diagonal?

   • 14 cm
   • 12 cm
   • 9.8 cm
   • 10 cm

10. A 13 m ladder leans against a vertical wall with its foot 5 m from the wall. How far up the wall does its top reach?

    • 18 m
    • 11 m
    • 12 m
    • 8 m

11. A cuboid measures 3 cm by 4 cm by 12 cm. What is the length of its space diagonal?

    • 13 cm
    • 15 cm
    • 19 cm
    • 17 cm

12. The base of a cuboid is a rectangle 4 cm by 7 cm. What is the length of the base diagonal, to 2 decimal places?

    • 7.50 cm
    • 10.50 cm
    • 8.06 cm
    • 11.00 cm

13. A point P is 4 m east and 3 m north of a point O. How far is P from O?

    • 12 m
    • 7 m
    • 6 m
    • 5 m

14. A right-angled triangle has hypotenuse 26 cm and one shorter side 10 cm. What is the other shorter side?

    • 24 cm
    • 16 cm
    • 22 cm
    • 36 cm

15. Why is a triangle with side lengths 6 cm, 8 cm and 11 cm not right-angled?

    • 6 + 8 ≠ 11
    • 6² + 11² ≠ 8²
    • 6 × 8 ≠ 11²
    • 6² + 8² ≠ 11²

16. A square has a diagonal of 10 cm. What is its side length, to 2 decimal places?

    • 14.14 cm
    • 7.07 cm
    • 8.66 cm
    • 5.00 cm

17. A cuboid has a square base of 6 cm by 6 cm and a space diagonal of 15 cm. What is its height, to 2 decimal places?

    • 13.50 cm
    • 12.37 cm
    • 9.00 cm
    • 15.00 cm

18. Points A(1, 2) and B(7, 10) lie on a coordinate grid. What is the distance AB?

    • 12 units
    • 14 units
    • 10 units
    • 8 units

19. What is the distance of the point P(2, 3, 6) from the origin in three dimensions?

    • 11 units
    • 7 units
    • 49 units
    • 5 units

20. A 10 m ladder leans on a wall with its foot 6 m out. The foot slides 2 m further out. How far does the top move down the wall?

    • 4 m
    • 3 m
    • 1 m
    • 2 m

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