2014 AMC 12B Problem 5

Doug constructs a square window using

8

equal-size panes of glass, as shown. The ratio of the height to width for 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?

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Solution

Let each pane have width

2x

and height

5x.

The window is

4

panes wide with

5

vertical borders, so its width is

4(2x) + 5\cdot2 = 8x+10.

It is

2

panes tall with

3

horizontal borders, so its height is

2(5x) + 3\cdot2 = 10x+6.

Setting width equal to height gives

8x+10 = 10x+6,

x=2

and the side length is

10\cdot2+6 = 26.

Thus, the correct answer is A.