GCSE Maths revision · Geometry and measures

Pythagoras' theorem

Foundation and Higher

The idea

In a right-angled triangle, $a^2 + b^2 = c^2$ , where $c$ is the hypotenuse, the longest side opposite the right angle.

Watch out Find the hypotenuse before you substitute: it is the side opposite the right angle.

Worked exampleCalculator allowed3 marks

The diagram shows a right-angled triangle.

Work out the length of the hypotenuse. Give your answer correct to 1 decimal place.

Pythagoras: the hypotenuse is opposite the right angle. $c^2 = 7^2 + 11^2 = 49 + 121 = 170$
$c = \sqrt{170} = 13.038\ldots$
Correct to 1 decimal place: 13.0 cm.

Answer 13.0 cm

Question 1Non-calculator2 marks

The diagram shows a triangle.

Is the triangle right-angled? You must show how you get your answer.

Question 2Non-calculator4 marks

The diagram shows a rectangle with one diagonal drawn.

(a) Work out the length of the diagonal.

(b) Work out how much shorter the diagonal is than the route along two sides of the rectangle.

Question 3Non-calculator3 marks

The diagram shows a rectangle with one of its diagonals.

The perimeter of the rectangle is 70 cm. The diagonal is 25 cm.

Work out the area of the rectangle.

You must show your working.

85 official questions in 81 papers since 2017. The latest:

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