How would I find the answer to...

A rectangular flat-screen computer monitor has a diagonal that measures 20 inches. The ratio of the length of the screen to the width of the screen is 4 to 3. What is the perimeter of the screen, in inches?

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

\(\displaystyle \frac{x}{y} = \frac{4}{3} \)

Or, \(\displaystyle x = \frac{4}{3}y \,\,\,\,\,\, (1)\)

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

\(\displaystyle x^2 + y^2 = 20^2 \,\,\,\,\,\,\, (2) \)

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.