Pythagoras' Theorem — Year 9 Practice Questions
Work through these Year 9 practice questions on Pythagoras' theorem. Try each one before revealing the worked solution.
Questions
In a right-angled triangle, which side is the hypotenuse?
A right-angled triangle has shorter sides 3 cm and 4 cm. Find the hypotenuse.
A right-angled triangle has shorter sides 6 cm and 8 cm. Find the hypotenuse.
A right-angled triangle has hypotenuse 13 cm and one shorter side 5 cm. Find the other side.
A right-angled triangle has shorter sides 5 cm and 12 cm. Find the hypotenuse.
A right-angled triangle has hypotenuse 10 cm and one side 6 cm. Find the other side.
A ladder 5 m long leans against a wall with its foot 3 m from the wall. How high up the wall does it reach?
Find the length of the diagonal of a rectangle 8 cm by 6 cm.
Answers & Worked Solutions
Question 1 Solution
Step 1: The hypotenuse is opposite the right angle.
Step 2: It is always the longest side.
Answer: The side opposite the right angle (the longest side)
Question 2 Solution
Step 1: 3² + 4² = 9 + 16 = 25.
Step 2: √25 = 5 cm.
Answer: 5 cm
Question 3 Solution
Step 1: 6² + 8² = 36 + 64 = 100.
Step 2: √100 = 10 cm.
Answer: 10 cm
Question 4 Solution
Step 1: 13² − 5² = 169 − 25 = 144.
Step 2: √144 = 12 cm.
Answer: 12 cm
Question 5 Solution
Step 1: 5² + 12² = 25 + 144 = 169.
Step 2: √169 = 13 cm.
Answer: 13 cm
Question 6 Solution
Step 1: 10² − 6² = 100 − 36 = 64.
Step 2: √64 = 8 cm.
Answer: 8 cm
Question 7 Solution
Step 1: The ladder is the hypotenuse: 5² − 3² = 25 − 9 = 16.
Step 2: √16 = 4 m.
Answer: 4 m
Question 8 Solution
Step 1: The diagonal is the hypotenuse: 8² + 6² = 64 + 36 = 100.
Step 2: √100 = 10 cm.
Answer: 10 cm
Build strong foundations in Pythagoras' Theorem
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