Problem
2008 AMC 12A 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? ![[asy]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);[/asy]](/static/aops/4994e8ffcb62ccc25ab593f3852cfd9b2fb7ba26.png)
\mathrm{(A)}\ 2\qquad\mathrm{(B)}\ 2.25\qquad\mathrm{(C)}\ 2.5\qquad\mathrm{(D)}\ 2.7\qquad\mathrm{(E)}\ 3
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