Help with Pythagoras

My brain has seized. Could someone help sort me out...

For a right-angled triangle, given a hypotenuse z and a ratio r, how do I calculate values of x and y such that x/y == r and (x*x) + (y*y) == (z*z)?

In other words, how do I change the aspect ratio of a prim face while keeping the length of the diagonal constant?

1. x*x + y*y = z*z

2. x/y = r

x = r y

3. r*r*y*y +y*y = z*z

(r*r + 1) . y*y = z*z

y*y = z*z / (r*r + 1)

y = sqrt(z*z / (r*r + 1))

Plug that in the original to solve for x

If you want x/y = r but x^2 + y^2 = z^2 then let

x = z*sin(t)
y = z*cos(t)

where t is arctan(r).

Now for any ratio r and fixed z you can find x and y.

Many thanks guys, it works a treat. I guess I should've paid more attention during maths lessons