Question

一个正方形图案中有 $8$ 块阴影方砖和 $17$ 块非阴影方砖。若在该正方形周围加上一圈阴影方砖来扩展图案，扩展后阴影方砖与非阴影方砖的比是多少？

Extend the square pattern of $8$ shaded and $17$ unshaded square tiles by attaching a border of shaded tiles around the square. What is the ratio of shaded tiles to unshaded tiles in the extended pattern?

$8:17$

$25:49$

$36:25$

$32:17$

$36:17$

答案：D

知识点：比与比例基本计数

难度评级：720

解答：

原图案是一个 $5\times5$ 的正方形。每边向外扩展一块方砖后，得到一个 $7\times7$ 的正方形，所以新增加的阴影边框有 $7^2-5^2=24$ 块方砖。加上原来的 $8$ 块阴影方砖，共有 $24+8=32$ 块阴影方砖。原来的 $17$ 块非阴影方砖不变，因此阴影方砖与非阴影方砖之比为 $32:17$ 。

所以正确答案是 D。

The original pattern is a $5\times5$ square. Extending it by one tile on every side makes a $7\times7$ square, so the new shaded border contains $7^2-5^2=24$ tiles. Together with the original $8$ shaded tiles, there are $24+8=32$ shaded tiles. The original $17$ unshaded tiles do not change, so the ratio of shaded tiles to unshaded tiles is $32:17.$

Thus, D is the correct answer.

2011 AMC 8 第 3 题

答案：D

难度评级：720

解答：

其他年份的第 3 题