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Pythagoras' theorem – practice for Years 8–9

Sample questions on Pythagoras' theorem with the right answer and a worked solution, from easy to hard. In the Pickles Academy app a child gets new questions of the same kind every time, so they can't just learn the answers by heart.

Subject
Maths
Year
Years 8–9
Curriculum area
Geometry and measures

Question types: Calculation with a picture · Pythagoras' theorem in word problems

Rule: Pythagoras' theorem

In a right-angled triangle c² = a² + b²; c is the hypotenuse, opposite the right angle.

Hypotenuse: c = √(a² + b²). A shorter side: b = √(c² − a²).

Example: a = 6 cm, b = 8 cm: c = √(36 + 64) = √100 = 10 cm

Watch out: √(36 + 64) is not 6 + 8. Add the squares first, then take the square root.

Sample questions

  1. Question 1 Easy

    A right-angled triangle has hypotenuse c = 34 cm and leg a = 16 cm. Work out the length of leg b.

    a = 16 cmb = ?c = 34 cm
    Show the solution
    Answer: 30 cm

    How it works: b = √(c² − a²) = √(1156 − 256) = 30 cm

  2. Question 2 Normal

    A walker goes 8 km due north and then 15 km due east. How far is she in a straight line from where she started?

    Show the solution
    Answer: 17 km

    How it works: √(64 + 225) = √289 = 17 km

  3. Question 3 Hard

    Work out the length of the hypotenuse c of the right-angled triangle.

    a = 8 cmb = 15 cmc = ?
    Show the solution
    Answer: 17 cm

    How it works: c = √(a² + b²) = √(64 + 225) = 17 cm

Related topics

All Maths topics

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