2014 AMC 10B Problems/Problem 5

Problem

Doug constructs a square window using 8 equal-size panes of glass, as shown. The ratio of the height to width of each pane is 5 : 2, and the borders around and between the panes are 2 inches wide. In inches, what is the side length of the square window?

$\textbf {(A) } 26 \qquad \textbf {(B) } 28 \qquad \textbf {(C) } 30 \qquad \textbf {(D) } 32 \qquad \textbf {(E) } 34$

Solution

We note that the total length must be the same as the total height because the window a square. Calling the width of each small rectangle $2x$ , and the height $5x$ , we can see that the length is composed of 4 widths and 5 bars of length 2. This is equal to two heights of the small rectangles as well as 3 bars of 2. Thus, $4(2x) + 5(2) = 2(5x) + 3(2)$ . We quickly find that $x = 2$ . The total side length is $4(4) + 5(2) = 2(10) + 3(2) = 26$ , or $\boxed{(A)}$ .

2014 AMC 10B (Problems • Answer Key • Resources)
Preceded by Problem 4	Followed by Problem 6
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2014 AMC 10B Problems/Problem 5

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