2014 AMC 10B Problem 5

Problem 5 of 25EasierAlgebra

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 height

5x

and width

2x

. Vertically, the window contains two pane heights and three horizontal borders, so its height is

10x+6

. Horizontally, it contains four pane widths and five vertical borders, so its width is

8x+10

. Because the window is square,

10x+6=8x+10

, so

x=2

. Therefore, the side length is

10(2)+6=26

inches. Thus, the correct answer is A .