AMC 12 2008a Problem 9

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?

unitsize(1mm);
filldraw((0,0)--(21.6,0)--(21.6,2.7)--(0,2.7)--cycle,grey,black);
filldraw((0,13.5)--(21.6,13.5)--(21.6,16.2)--(0,16.2)--cycle,grey,black);
draw((0,0)--(21.6,0)--(21.6,16.2)--(0,16.2)--cycle);

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