Size of Television

First we write down the Pythagorean theorem as $$a^2+b^2 = c^2$$ where $a$ is the height and $b$ is the width. Now the ratio is given as $$\frac{b}{a} = \frac{16}{9}$$ Solving this equation for $b$ and inserting into the equation stated above, we obtain for the height: $$a = \frac{c}{\sqrt{4.16}} = 29.14\,\mathrm{cm}$$ Now we use again the Pythagorean theorem to calculate $b$: $$b = \sqrt{c^2 - a^2} = 53.66\,\mathrm{cm}$$