Question

The sides of a right triangle are (x-5) (x+2) (x+3). solve for x.

Can someone pls help me on this problem

Answer 1

x = 10.

Explanation:

The longest side , the hypotenuse = x + 3 because the lengths of the sides are positive.

So, by Pythagoras:

(x + 3)^2 = (x - 5)^2 + (x + 2)^2

x^2 + 6x + 9 = x^2 - 10x + 25 + x^2 + 4x + 4

0 = 2x^2 - x^2 - 10x + 4x - 6x + 29 - 9

x^2 - 12x + 20 = 0

(x - 10)(x - 2) = 0

x = 2, 10.

x cannot be 2 because that would make one side = 2- 5 = -3 so the answer is x = 10.