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 $2$ 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：比与比例一次方程矩形

难度评级：1400

解答：

设每块玻璃片宽 $2x$ ，高 $5x$ 。窗户横向有 $4$ 块玻璃片和 $5$ 条竖向边框，所以宽为 $4(2x) + 5\cdot2 = 8x+10$ 。

窗户纵向有 $2$ 块玻璃片和 $3$ 条横向边框，所以高为 $2(5x) + 3\cdot2 = 10x+6$ 。

令宽等于高，得到 $8x+10 = 10x+6$ ，所以 $x=2$ ，边长为 $10\cdot2+6 = 26$ 。

所以正确答案是 A。

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 第 5 题

答案：A

难度评级：1400

解答：

其他年份的第 5 题