If the legs of a right triangle are x and 3x+y, and the hypotenuse is 4x-y, what is the ratio of x to y?

x ^2 + (3x + y) ^ 2 = (4x - y ) ^2
x ^2 + 9x^2 + 6xy + y ^ 2 = 16x ^2 -8xy + y ^2
-6x ^2 + 14xy = 0
x = 0 (not good answer. This leg is zero. )
or 14y = 6x, x /y = 14 / 6 = 7/ 3

For a right triangle, remember the Pythagorean theorem of

a^2 + b^2 = c^2

and plug in for a and b, x and 3x+y, and for c, 4x-y supplied to you.

You should then be able to simplify to what x/y is.