AMC 10 2008a Problem 14

Older television screens have an aspect ratio of $4: 3$. That is, the ratio of the width to the height is $4: 3$. The aspect ratio of many movies is not $4: 3$, so they are sometimes shown on a television screen by "letterboxing" - darkening strips of equal height at the top and bottom of the screen, as shown. Suppose a movie has an aspect ratio of $2: 1$ and is shown on an older television screen with a $27$-inch diagonal. What is the height, in inches, of each darkened strip?

$\mathrm{(A)}\ 2 \mathrm{(B)}\ 2.25 \mathrm{(C)}\ 2.5 \mathrm{(D)}\ 2.7 \mathrm{(E)}\ 3$