2003 AMC 10B Problem 6

Below is the professionally curated solution for Problem 6 of the 2003 AMC 10B, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2003 AMC 10B solutions, or check the answer key.

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Concepts:Pythagorean Triple ratio and proportion

Difficulty rating: 1000

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?

$20$

$20.5$

$21$

$21.5$

$22$

Solution:

Since the length and height are in ratio $4:3,$ the length, height, and diagonal form a $4:3:5$ right triangle. The diagonal is $27,$ so the horizontal length is $\dfrac{4}{5}(27)=21.6,$ which is closest to $21.5.$

Thus, the correct answer is D.

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