Pythagorean Theorem Quiz
Test your knowledge of Pythagorean Theorem for GCSE Maths, with this quiz.
This quiz consists of 15 questions, including multiple-choice and short-answer questions on the topic of Pythagorean Theorem for GCSE Maths.
For multiple-choice questions, choose the correct answer. Scroll down to begin the quiz.
Questions
Which of the following represents the Pythagorean Theorem correctly?
Incorrect
Incorrect
Incorrect
Correct
In a right-angled triangle, if the two shorter sides are 6 cm and 8 cm, what is the length of the hypotenuse?
Correct
Incorrect
Incorrect
Incorrect
The Pythagorean Theorem applies only to which type of triangle?
Incorrect
Incorrect
Correct
Incorrect
If c² = a² + b², which side does ‘c’ represent?
Incorrect
Incorrect
Correct
Incorrect
If a triangle has sides of lengths 5 cm, 12 cm and 13 cm, is it a right-angled triangle?
Correct
Incorrect
Incorrect
Incorrect
Calculate the length of the hypotenuse if the other sides are 9 cm and 12 cm.
Answer:
c² = 9² + 12²
= 81 + 144 = 225
$c = \sqrt{225} = 15cm$
One side of a right-angled triangle is 7 cm, the hypotenuse is 25 cm. Find the other side.
Answer:
$b^2 = 25^2 - 7^2$
$= 625 - 49 = 576$
$b = \sqrt{576} = 24cm$
In a triangle, the sides are 10 cm and 24 cm, and the hypotenuse is unknown. Find it.
Answer:
$c^2 = 10^2 + 24^2$
$ = 100 + 576 = 676$
$c = \sqrt{676} = 26cm$
Find the missing side: one leg is 5 cm, hypotenuse is 13 cm.
Answer:
$b^2 = 13^2 - 5^2$
$= 169 - 25 = 144$
$b = \sqrt{144} = 12cm$
A ladder leans against a wall. It reaches 4 m up the wall and is 3 m from the base. How long is the ladder?
Answer:
$c^2 = 3^2 + 4^2$
$= 9 + 16 = 25$
$c = \sqrt{25} = 5cm$
Calculate the height of a triangle if the base is 10 cm and the hypotenuse is 12 cm.
Answer:
$h^2 = 12^2 - 10^2$
$= 144 - 100 = 44$
$h = \sqrt{44} \approx 6.63cm$
Two sides of a triangle are 11 cm and 60 cm, and the hypotenuse is 61 cm. Is it a right-angled triangle?
Answer: Yes
Check: $11^2 + 60^2$
$= 121 + 3600 = 3721$
$= 61^2$
The diagonal of a square is 10 cm. What is the length of each side?
Answer:
$s^2 + s^2 = 10^2 = 100$
$2s^2 = 100 \Rightarrow s^2 = 50 \Rightarrow s = \sqrt{50} \approx 7.07cm$
If a triangle has sides 9 cm, 40 cm, and 41 cm, is it a right-angled triangle?
Answer: Yes
$9^2 + 40^2$
$= 81 + 1600 = 1681 = 41^2$
A triangle has a hypotenuse of 17 cm and one side of 8 cm. Find the third side.
Answer:
$b^2 = 17^2 - 8^2$
$= 289 - 64 = 225$
$b = \sqrt{225} = 15cm$
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