Junior Secondary · Mathematics

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

Determine which of the following sets of numbers can represent the lengths of the sides of a right-angled triangle.

Question 2

1 mark

A point \(A\) has coordinates \((-5, 2)\) and point \(B\) has coordinates \((7, -3)\). What is the distance between point \(A\) and point \(B\)?

Question 3

1 mark

A small rectangular gift box has dimensions \( 2 \text{ cm} \) by \( 3 \text{ cm} \) by \( 6 \text{ cm} \). What is the distance between the two farthest points inside the box?

Question 4

1 mark

In a right-angled triangle, the lengths of the two legs are \( 10 \text{ cm} \) and \( 24 \text{ cm} \). What is the length of the hypotenuse?

Question 5

1 mark

In the figure, \(ABCD\) is a rectangle with \(AB = 12\text{ cm}\). If the length of the diagonal \(AC\) is \(20\text{ cm}\), find the area of the rectangle.

Question 6

2 marks

Find the length of the hypotenuse of a right-angled triangle whose legs are \( 12 \text{ cm} \) and \( 35 \text{ cm} \) long.

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Question 7

4 marks

A hiker travels \(12 \text{ km}\) due North and then \(9 \text{ km}\) due East. From that position, she travels another \(8 \text{ km}\) due North and \(12 \text{ km}\) due East. Calculate the straight-line distance, in \(\text{km}\), from her starting point to her final destination.

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Question 8

6 marks

In the figure, \(ABCD\) is a rectangle with \(AB = 24\text{ cm}\) and \(BC = 18\text{ cm}\). A point \(E\) lies on the diagonal \(AC\) such that \(AE:EC = 2:1\).
(a) Calculate the length of the diagonal \(AC\).
(b) Find the length of the segment \(BE\) correct to 1 decimal place.

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Question 9

4 marks

A rectangular swimming pool is 15 meters long and 8 meters wide. A swimmer decides to swim diagonally from one corner to the opposite corner. How far does the swimmer travel in one diagonal lap?

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Question 10

5 marks

A triangular garden \( ABC \) has side lengths \( AB = 9 \text{ m} \), \( BC = 12 \text{ m} \), and \( AC = 15 \text{ m} \).

(a) Using the converse of Pythagoras’ Theorem, show that \( \triangle ABC \) is a right-angled triangle. Which angle is the right angle?

(b) Calculate the area of the triangular garden.

(c) If a straight path is to be built from vertex \( B \) to the side \( AC \) such that the path is perpendicular to \( AC \), find the length of this path.

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

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