The sides of a triangle are of lenths x*-y*, x*+y* and 2xy units respectively. Prove that the triangle is a right angled triangle

Answer 1

You must mean:
sides are x^2 - y^2 , x^2 + y^2 , and 2xy

assume x^2+y^2 is the hypotenuse

then
(x^2-y^2)^2 + (2xy)^2 = (x^2+y^2)^2
LS = x^4 - 2x^2y^2 + y^4 + 4x^2y^2
= x^4 + 2x^2y^2 + y^4

RS = x^4 + 2x^2y^2 + y^4
= LS

Q.E.D.