Question

Find the expression that represents the length of the hypotenuse of a right triangle whose legs measure 2x^2 - y^2 and 2xy.

Answer 1

By pythagorean theorem,

$h^2=(2x^2-y^2)^2+(2xy)^2$

First simplify RHS,

$h^2=4x^4-4x^2y^2+y^4+4x^2y^2$

$h^2=4x^4+y^4$

Take square root of both sides,

$h=\sqrt{4x^4+y^4}$

So the answer is A.

Hope this helps :)