Question

八块 $1 \times 1$ 的正方形瓷砖拼成一个图形，其外边界周长为 $14$ 个单位。再加入两块同样大小的瓷砖，使每块新增瓷砖至少有一条边与原来某个正方形的一条边重合。下列哪一个可能是新图形的周长？

Eight $1 \times 1$ square tiles are arranged so their outside edges form a polygon with a perimeter of $14$ units. Two additional tiles of the same size are added to the figure so that at least one side of each added tile is shared with a side of one of the original squares. Which of the following could be the perimeter of the new figure?

$15$

$17$

$18$

$19$

$20$

答案：C

知识点：周长分类讨论

难度评级：1170

解答：

一块只共享一条边的新增瓷砖会使周长增加 $2$ ：四条新边中有两条因共享边而不在外边界上。若共享两条边，则周长增加 $0$ 。

加入两块瓷砖后，周长可能增加 $0$ 、 $2$ 或 $4$ ，新周长可能为 $14$ 、 $16$ 或 $18$ 。选项中只有 $18$ 可能。

所以正确答案是 C。

A tile that shares exactly one side adds $2$ to the perimeter (four new edges minus two hidden), while a tile sharing two sides adds $0.$

With two added tiles the perimeter can change by $0,$ $2,$ or $4,$ giving new perimeters of $14,$ $16,$ or $18.$ Of the choices, only $18$ is possible.

Thus, the correct answer is C .

1992 AMC 8 第 22 题

答案：C

难度评级：1170

解答：

其他年份的第 22 题