2014 AMC 12B 第 5 题
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所有题目均经美国数学协会（MAA）官方合法授权使用。
5.
Doug 用 块大小相同的玻璃片制作一个正方形窗户，如图所示。每块玻璃片的高宽比为 ，玻璃片周围和之间的边框宽 英寸。这个正方形窗户的边长是多少英寸？
Doug constructs a square window using equal-size panes of glass, as shown. The ratio of the height to width for each pane is and the borders around and between the panes are inches wide. In inches, what is the side length of the square window?
小提示：
设每块玻璃片宽 ，高 。
Let each pane be wide and tall
大提示：
窗户宽 ，高 ，二者相等。
The window’s width equals its height
解答：
设每块玻璃片宽 ，高 。窗户横向有 块玻璃片和 条竖向边框，所以宽为 。
窗户纵向有 块玻璃片和 条横向边框，所以高为 。
令宽等于高，得到 ，所以 ，边长为 。
所以正确答案是 A。
Let each pane have width and height The window is panes wide with vertical borders, so its width is
It is panes tall with horizontal borders, so its height is
Setting width equal to height gives so and the side length is
Thus, the correct answer is A.
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