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2008 AMC 12A Question 9

AMC12 · 2008 AMC 12A

Question 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?

Question illustration
  1. $2$
  2. $2.25$
  3. $2.5$
  4. $2.7$
  5. $3$