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2003 AMC 12B Problem 5

Problem 5 of 25EasierGeometryArithmetic

Many television screens are rectangles that are measured by the length of their diagonals. The ratio of the horizontal length to the height in a standard television screen is 4:3.4 : 3. The horizontal length of a 2727-inch television screen is closest, in inches, to which of the following?

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Solution

A rectangle with side ratio 4:34 : 3 has height, length, and diagonal in ratio 3:4:5.3 : 4 : 5. With diagonal 27,27, the horizontal length is 45(27)=21.6, \frac{4}{5}(27) = 21.6, which is closest to 21.5.21.5. Thus, the correct answer is D.
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Tagged: Pythagorean Triple · ratio and proportion

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