Question

Doug 用 $8$ 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 $5 : 2$ ，玻璃片周围和之间的边框宽度都是 $2$ 英寸。这个正方形窗户的边长是多少英寸？

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?

$\ 26$

$\ 28$

$\ 30$

$\ 32$

$\ 34$

答案：A

知识点：比与比例一次方程

难度评级：1280

解答：

设每块玻璃的高为 $5x$ ，宽为 $2x$ 。竖直方向上，窗户包含两块玻璃的高度和三条横框，所以高度为 $10x+6$ 。水平方向上，它包含四块玻璃的宽度和五条竖框，所以宽度为 $8x+10$ 。

因为窗户是正方形， $10x+6=8x+10$ ，所以 $x=2$ 。

因此边长为 $10(2)+6=26$ 英寸。

所以正确答案是 A。

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 第 5 题

答案：A

难度评级：1280

解答：

其他年份的第 5 题