AMC 8 1992 Problem 22
AMC8 1992 年第 22 题
面积与周长（综合）★★★☆☆
Eight square tiles are arranged as shown 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 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?
八块 的方形瓷砖如图所示排列，其外缘形成一个周长为 14 个单位的多边形。在原图形上添加两块同样大小的瓷砖，使得每块新瓷砖至少有一条边与原图形中某块正方形的边共边。新图形的周长可能是以下哪个？
- A.15
- B.17
- C.18
- D.19
- E.20
正确答案 · Correct Answer
C
解析 · Solution
Solution 1
One such figure would be
The perimeter of this figure is .
If we attach a square to one side, one side will be covered, and 3 more sides will be added, resulting in a +2 perimeter. If we attach a square to two sides, 2 sides are covered and 2 sides are attached, so the perimeter don't change. There is no possibility of attaching a square to 3 sides, so we can get 14,16,18 as the perimeter so the only answer is .
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