A right triangle has a hypotenuse of length x + 2 and two legs of length x and x + 1. Find the lengths of all the sides of the triangle.

Answer 1

5, 4 and 3 are the 3 sides, a Pythagorean Triple

(x+2)^2 = x^2 + (x+1)^2

x^2 +4x +4 = x^2 +x^2 +2x +1

x^2 -2x -3 = 0

(x-3)(x+1) = 0

x = 3 or -1

x+1 = 4 or 0

x+2 = 5 or 1

sides are 3,4, and 5, or theoretically also -1, 0 and 1