2003 AMC 12B Problem 5

Below is the professionally curated solution for Problem 5 of the 2003 AMC 12B, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2003 AMC 12B solutions, or check the answer key.

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Concepts:Pythagorean Tripleratio and proportion

Difficulty rating: 1050

5.

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?

2020

20.520.5

2121

21.521.5

2222

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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