The side lengths of a right triangle measure x, x + y, and x + 2y units where 0 < y < x. What is the value of y/x? Express your answer as a common fraction
(x)^2 + (x+y)^2 = (x + 2y)^2 (this is the pythagreon theorum)
x^2 + x^2 + y^2 + 2xy = x^2 + 4y^2 + 4xy
2x^2 + y^2 + 2xy = x^2 + 4y^2 + 4xy
x^2 = 3y^2 + 2xy
So we're looking for xy, and we could solve for it, but let's just say x = 1 for simplicity.
1^2 = 3*y^2 + 2(1)y
1 = 3y^2 + 2y.
y = 1/3.
So y/x = 1/3/1 = 1/3.
I hope this helped. :)))