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?

$\ 26$

$\ 28$

$\ 30$

$\ 32$

$\ 34$

Answer: A

Concepts:ratio and proportion linear equation

Difficulty rating: 1280

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 .

2014 AMC 10B Problem 5

Answer: A

Difficulty rating: 1280

Solution:

Problem 5 in Other Years