2003 AMC 10B Problems/Problem 6

Problem

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?

$\textbf{(A) } 20 \qquad\textbf{(B) } 20.5 \qquad\textbf{(C) } 21 \qquad\textbf{(D) } 21.5 \qquad\textbf{(E) } 22$

Solution

Because the legs are in the ratio of $4 : 3$ , let one leg be $4x$ and the other be $3x$ .

Then we use the Pythagorean Theorem:

$(4x)^2+(3x)^2=27^2$

$16x^2+9x^2=729$

$25x^2=729$

$x^2=\frac{729}{25}$

$x=\frac{27}{5}$

$x=5.4$

The horizontal length is $5.4\cdot4=21.6$ , which is closest to $\boxed{21.5 \text{ (D)}}$ .

2003 AMC 10B (Problems • Answer Key • Resources)
Preceded by Problem 5	Followed by Problem 7
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
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2003 AMC 10B Problems/Problem 6

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