AMC8 1992

AMC8 1992 · Q22

AMC8 1992 · Q22. It mainly tests Area & perimeter.

Eight 1 × 1 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?

八个1×1正方形瓷砖按所示排列，它们的外部边缘形成一个周长为14单位的的多边形。添加两个相同大小的瓷砖，使得每个瓷砖至少有一边与原图中一个正方形的边共享。新图形的周长可能是以下哪一个？

(A) 15 15

(B) 17 17

(D) 19 19

(E) 20 20

Answer

Correct choice: (C)

正确答案：（C）

Solution

Answer (C): When a new tile is added to the original figure, it may have one or two sides in common with the given tiles, as shown. When a tile shares one side, the original perimeter is increased by 2. When a tile shares two sides, there is no change in the perimeter. By adding two tiles, the only possible changes to the perimeter are increases of 0, 2 or 4. Hence, the possible value of the perimeter are 14, 16, or 18.

答案 (C)：向原图添加新瓦片时，新瓦片可能与现有瓦片共一边或两边。如图所示。共一边时，周长增加2；共两边时，周长不变。添加两块瓦片，周长仅可能增加0、2或4。因此可能周长为14、16或18。

Topics

GE.007 Area & perimeter