Question

In a right triangle, one of the legs is 5 cm smaller than the hypotenuse, and the other leg is 10 cm smaller than the hypotenuse. Find the length of the hypotenuse.

Answer 1

25 cm.

Explanation:

If the hypotenuse is x cm long the 2 legs are x-5 and x-10 cm long.

So by the Pythagoras theorem:

x^2 = (x - 5)^2 + (x - 10)^2

x^2 = x^2 - 10x + 25 + x^2 - 20x + 100

x^2 - 30x + 125 = 0

(x - 5)(x - 25) = 0

x = 5, 25

We can discard x = 5 because that would make the lengths of the legs negative so the hypotenuse = 25 cm long.