Letterboxing
Source: AMC 12 2008A Problem 9
February 17, 2008
ratioAMC
Problem Statement
Older television screens have an aspect ratio of . That is, the ratio of the width to the height is . The aspect ratio of many movies is not , 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 and is shown on an older television screen with a -inch diagonal. What is the height, in inches, of each darkened strip?
[asy]unitsize(1mm);
defaultpen(linewidth(.8pt));
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((0,2.7)--(0,13.5));
draw((21.6,2.7)--(21.6,13.5));[/asy]