2014 AMC 12B Problems/Problem 5
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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. Unknown error_msg)
Solution
Let the height of the panes equal , and let the width of the panes equal
. Now notice that the total width of the borders equals
, and the total height of the borders is
. We have
Now, the total side length of the window equals