Question

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?

$26$

$28$

$30$

$32$

$34$

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 $8x+10 = 10x+6,$ so $x=2$ and the side length is $10\cdot2+6 = 26.$

Thus, the correct answer is A.

2014 AMC 12B Problem 5

Solution:

Problem 5 in Other Years