2003 AMC 12B Problem 5

Problem 5 of 25EasierAlgebra Geometry

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.

The horizontal length of a

27

-inch television screen is closest, in inches, to which of the following?

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Solution

A rectangle with side ratio

4 : 3

has height, length, and diagonal in ratio

3 : 4 : 5.

With diagonal

27,

the horizontal length is

\frac{4}{5}(27) = 21.6,

which is closest to

21.5.

Thus, the correct answer is D.

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