Practice Pythagorean theorem
In a right-angled triangle, the squares of the two shorter sides add up to the square of the hypotenuse: a² + b² = c².
The rule does not apply to other triangles.
Exercises with solutions
First check that the triangle is right-angled. The hypotenuse is opposite the right angle. Substitute the known lengths into a² + b² = c² and take the square root at the end.
Exercise 1
A right-angled triangle has legs of 6 cm and 8 cm. Find its hypotenuse.
Show solution and working
10 cm
c² = 6² + 8² = 100 cm², so c = 10 cm.
Exercise 2
The hypotenuse is 13 cm and one leg is 5 cm. Find the other leg.
Show solution and working
12 cm
b² = 13² − 5² = 144 cm², so b = 12 cm.
Exercise 3
A rectangle measures 9 cm by 12 cm. Find its diagonal.
Show solution and working
15 cm
The diagonal forms a right-angled triangle: d² = 9² + 12² = 225 cm². Therefore d = 15 cm.
Exercise 4
Can a triangle with sides 5 cm, 6 cm and 8 cm be right-angled?
Show solution and working
No.
The longest side would be the hypotenuse. But 5² + 6² = 61, while 8² = 64, so the equality does not hold.
Common mistake
The hypotenuse is always opposite the right angle. Subtract squares when finding a missing leg; the theorem applies only to right-angled triangles.
Keep learning with MatheJump
Create a free account and explore math practice. Choose from the available exercises to suit your learning needs.