1992 AMC 8 第 22 题
先试着解答 1992 AMC 8 第 22 题，然后核对你的答案与精心整理的解答，解答来自 LIVE by Po-Shen Loh。你也可以参加完整限时模拟考试、查看全部 1992 AMC 8 解答，或核对答案。
所有题目均经美国数学协会（MAA）官方合法授权使用。
22.
如图，八块 的正方形瓷砖拼成一个图形，其外边界周长为 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图中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 square tiles are arranged as shown so their outside edges form a polygon with a perimeter of 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 squares in the original figure. Which of the following could be the perimeter of the new figure?
小提示：
新加一块瓷砖若只共享一条边，周长增加 ；若共享两条边，周长增加 。
Adding a tile that shares exactly one side changes the perimeter by ; sharing two sides changes it by
大提示：
加两块瓷砖时，总变化量可能是 、 或 ；把它们加到 上。
With two added tiles, the total change can be or ; add these to
解答：
一块只共享一条边的新增瓷砖会使周长增加 ：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 。
加入两块瓷砖后，周长可能增加 、 或 ，新周长可能为 、 或 。选项中只有 可能。
所以正确答案是 C。
A tile that shares exactly one side adds to the perimeter (four new edges minus two hidden), while a tile sharing two sides adds
With two added tiles the perimeter can change by or giving new perimeters of or Of the choices, only is possible.
Thus, the correct answer is C .
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