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2003 AMC 10B Problem 6

Problem 6 of 25EasierAlgebraGeometry

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

Since the length and height are in ratio 4:3,4:3, the length, height, and diagonal form a 4:3:54:3:5 right triangle. The diagonal is 27,27, so the horizontal length is 45(27)=21.6,\dfrac{4}{5}(27)=21.6, which is closest to 21.5.21.5. Thus, the correct answer is D.

More practice

Concepts: Pythagorean Triple · ratio and proportion

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.