2014 AMC 10B Problems/Problem 5
Problem
Doug constructs a square window using equal-size panes of glass, as shown. The ratio of the height to width for each pane is , and the borders around and between the panes are inches wide. In inches, what is the side length of the square window? $\textbf{(A)}\ 26\qquad\textbf{(B)}\ 28\qquad\textbf{(C)}\ 30\qquad\textbf{(D)}}\ 32\qquad\textbf{(E)}\ 34$ (Error compiling LaTeX. ! Extra }, or forgotten $.)
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 , and the height , 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, . We quickly find that . The total side length is , or .
See Also
2014 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 4 |
Followed by Problem 6 | |
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All AMC 10 Problems and Solutions |
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