A square television screen measures 39 inches across the diagonal. Find the dimensions of the screen. Round your answer to two decimal places.

A) $19.5\text{ inches }\times 19.5\text{ inches }$
B) $30.88\text{ inches }\times 30.88\text{ inches }$
C) $27.58\text{ inches }\times 27.58\text{ inches }$
D) $8.83\text{ inches }\times 8.83\text{ inches }$
E) $29.68\text{ inches }\times 29.68\text{ inches }$

Let the length and width of the screen be $x$. We know that the diagonal is $39$ inches. We can create a right triangle with the length, width, and diagonal as the legs and hypotenuse. Using the Pythagorean theorem, we have:
$$x^2+x^2=39^2$$
$$2x^2=1521$$
$$x^2=760.5$$
$$x=\sqrt{760.5}\approx 27.58$$
Therefore, the dimensions of the screen are approximately $27.58$ inches by $27.58$ inches, so the answer is (C).