Question

The size of a computer monitor is given by the length of the diagonal of the screen. The ratio of the height to the width of wide-screen monitors is 9:16. Find expressions for the width and height of a wide-screen monitor in terms of the length of its diagonal.

Answer 1

So if x is the diagonal, x^2=w^2+h^2 The height is 9/16 of the width, or h=9w/16, so\[x^2=w^2+h^2=w^2+81w^2/256=337w^2/256\implies x=w \sqrt{337}/16\]\[\implies w=16x \sqrt{337}/337 \implies h=9x \sqrt{337}/337 \]