Lesson T4.6.1

T4.6.1 Pythagoras' theorem Quiz: KS3 Maths, Unit 4

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson T4.6.1, Pythagoras' theorem: 20 multiple choice questions for the KS3 Maths (National Curriculum), Unit 4: Geometry and measures, written with Revision Ninja.

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The 20 questions

  1. Pythagoras' theorem applies to which triangles?

    • Any triangle
    • Right-angled triangles
    • Equilateral triangles only
    • Circles only

  2. What is the hypotenuse of a right-angled triangle?

    • The side next to the right angle, always the base
    • The base of the triangle, always drawn horizontal
    • The shortest side, opposite the smallest angle
    • The longest side, opposite the right angle

  3. Which formula is Pythagoras' theorem?

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

  4. A right-angled triangle has legs 3 cm and 4 cm. What is the hypotenuse?

    • 7 cm
    • 5 cm
    • 12 cm
    • 25 cm

  5. A right-angled triangle has legs 6 cm and 8 cm. What is the hypotenuse?

    • 48 cm
    • 100 cm
    • 10 cm
    • 14 cm

  6. A right-angled triangle has hypotenuse 13 cm and one leg 5 cm. What is the other leg?

    • 8 cm
    • 12 cm
    • 169 cm
    • 18 cm

  7. A 5 m ladder leans against a wall with its foot 3 m from the wall. How high up the wall does it reach?

    • 2 m
    • 34 m
    • 4 m
    • 8 m

  8. Which set of lengths could be the sides of a right-angled triangle?

    • 5, 12 and 13
    • 3, 4 and 6
    • 4, 5 and 6
    • 2, 3 and 4

  9. Is a triangle with sides 7, 24 and 25 right-angled?

    • Only if the triangle is isosceles
    • No, because 25 is too short
    • No, because 7 + 24 is not 25
    • Yes, because 7² + 24² = 25²

  10. A right-angled triangle has a leg of 9 cm and a hypotenuse of 15 cm. What is the other leg?

    • 6 cm
    • 24 cm
    • 225 cm
    • 12 cm

  11. A ladder rests against a wall. It is 10 m long and its foot is 6 m from the wall. How high does it reach?

    • 16 m
    • 64 m
    • 4 m
    • 8 m

  12. A square has sides of 7 cm. What is its diagonal, to 1 decimal place?

    • 14 cm
    • 49 cm
    • 9.9 cm
    • 7 cm

  13. A rectangle is 9 cm by 12 cm. What is the length of its diagonal?

    • 15 cm
    • 108 cm
    • 3 cm
    • 21 cm

  14. A right-angled triangle has a hypotenuse of 17 cm and a leg of 8 cm. What is the other leg?

    • 9 cm
    • 25 cm
    • 225 cm
    • 15 cm

  15. An isosceles triangle has sides 5 cm, 5 cm and a base of 6 cm. What is its height?

    • 3 cm
    • 8 cm
    • 4 cm
    • 5 cm

  16. Which rearrangement gives the leg b in a right-angled triangle?

    • b = √(c² - a²)
    • b = √(c² + a²)
    • b = c² - a²
    • b = c - a

  17. Can Pythagoras' theorem be used on a triangle with no right angle?

    • Yes, if the triangle is isosceles with two equal sides
    • Yes, it always works, whatever the angles are
    • No, it only works for right-angled triangles
    • Yes, if the triangle is equilateral with equal sides

  18. A rectangular floor is 6 m by 8 m. What is the length of its diagonal?

    • 2 m
    • 14 m
    • 48 m
    • 10 m

  19. A kite string is 25 m long and reaches a point 24 m above the ground. How far horizontally is the kite from the child holding the string?

    • 1 m
    • 49 m
    • 31 m
    • 7 m

  20. A right-angled triangle has legs 5 cm and 5 cm. What is the hypotenuse, to 2 decimal places?

    • 10 cm
    • 25 cm
    • 7.07 cm
    • 5 cm

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