Let x be the length of the screen. Let y be the width. Then, given the ratio, we may say that:

Or,

Now, using pythagorus to relate the length of the diagonal to the length of the sides we get:

Equations (1) and (2) are two equations in two unknowns, so you should be able to solve them by substituting (1) into (2), then solving for x, and then using your solution for x in equation (1) to solve for y.