Cambridge IGCSE · Mathematics (0580)

Pythagoras’ theorem: Practice Questions

5 multiple-choice questions marked as you go, and 5 written questions with worked solutions. All on Pythagoras’ theorem.

10 questions26 marksFree, no account

Question 1

1 mark

A right-angled triangle has two shorter sides with lengths of 9 cm and 12 cm. Calculate the length of the hypotenuse.

Question 2

1 mark

Calculate the distance between the points \(P(2, -3)\) and \(Q(6, 0)\) on a Cartesian coordinate grid.

Question 3

1 mark

A rectangular box (cuboid) has a length of 12 cm, a width of 4 cm, and a height of 3 cm. Calculate the length of the internal diagonal that connects a bottom corner to the opposite top corner.

Question 4

1 mark

A rectangular gate is 3 metres wide and 4 metres high. Calculate the length of a diagonal wooden brace that needs to be attached from one corner to the opposite corner.

Question 5

1 mark

An isosceles triangle has two equal sides of length 10 cm and a base of length 12 cm. Calculate the vertical height of this triangle.

Question 6

2 marks

A right-angled triangle has a hypotenuse of length \(13\text{ cm}\) and one side of length \(5\text{ cm}\). Calculate the length of the other side.

Write your answer out first, then check it against the worked solution.

Question 7

4 marks

In the diagram, \(AC\) is perpendicular to \(BD\). Given that \(AB = 15\text{ cm}\), \(BC = 9\text{ cm}\), and \(CD = 16\text{ cm}\), calculate the length of \(AD\).

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Question 8

6 marks

In a circle with centre \( O \), two parallel chords \( AB \) and \( CD \) are on the same side of the centre. Chord \( AB \) has length 16 cm and is 6 cm from \( O \). Chord \( CD \) is 3 cm from \( O \). Calculate the length of chord \( CD \), giving your answer to 1 decimal place.

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Question 9

4 marks

A ladder of length \(6.5\text{ m}\) rests against a vertical wall. The base of the ladder is placed on horizontal ground, \(2.5\text{ m}\) away from the wall.

(a) Calculate the height up the wall reached by the top of the ladder.

(b) The ladder slips down so that its top is now \(5.2\text{ m}\) above the ground. Calculate how far the base of the ladder is now from the wall.

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Question 10

5 marks

The diagram shows a right-angled trapezium \(ABCD\) where angle \(A = 90^\circ\) and angle \(B = 90^\circ\). The side lengths are \(AB = 12\text{ cm}\), \(AD = 18\text{ cm}\), and \(BC = 9\text{ cm}\).

(a) By constructing a perpendicular from \(C\) to \(AD\), calculate the length of side \(CD\).

(b) Calculate the total perimeter of trapezium \(ABCD\).

(c) Calculate the area of trapezium \(ABCD\).

Write your answer out first, then check it against the worked solution.

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