AMC12 2014 B

AMC12 2014 B · Q5

AMC12 2014 B · Q5. It mainly tests Linear equations, Area & perimeter.

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?

Doug 使用 8 块相同大小的玻璃板构成一个正方形窗户，如图所示。每块玻璃板的宽度与高度之比为 5 : 2，玻璃板之间和周围的边框宽 2 英寸。正方形窗户的边长是多少英寸？

(A) 26 26

(B) 28 28

(D) 32 32

(E) 34 34

Answer

Correct choice: (A)

正确答案：（A）

Solution

Answer (A): Denote the height of a pane by $5x$ and the width by $2x$. Then the square window has height $2\cdot 5x+6$ inches and width $4\cdot 2x+10$ inches. Solving $2\cdot 5x+6=4\cdot 2x+10$ gives $x=2$. The side length of the square window is $26$ inches.

答案（A）：设一块窗格的高度为 $5x$，宽度为 $2x$。则该正方形窗户的高度为 $2\cdot 5x+6$ 英寸，宽度为 $4\cdot 2x+10$ 英寸。解方程 $2\cdot 5x+6=4\cdot 2x+10$ 得 $x=2$。该正方形窗户的边长为 $26$ 英寸。

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