Answer:
x = 10.
Step-by-step 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.
