Difference between revisions of "2014 AMC 10B Problems/Problem 5"
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==Solution== | ==Solution== |
Revision as of 11:53, 13 August 2014
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
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 | |
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 | ||
All AMC 10 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.