AMC8 2002

AMC8 2002 · Q23

AMC8 2002 · Q23. It mainly tests Casework, Area & perimeter.

A corner of a tiled floor is shown. If the entire floor is tiled in this way and each of the four corners looks like this one, then what fraction of the tiled floor is made of darker tiles?

展示了一个铺砖地板的一个角落。如果整个地板都以这种方式铺砖，并且四个角落看起来都像这个，那么铺砖地板中有多少分数是深色瓷砖？

(A) $\frac{1}{3}$ $\frac{1}{3}$

(B) $\frac{4}{9}$ $\frac{4}{9}$

(D) $\frac{5}{9}$ $\frac{5}{9}$

(E) $\frac{8}{9}$ $\frac{8}{9}$

Answer

Correct choice: (B)

正确答案：（B）

Solution

The 6 × 6 square in the upper left-hand region is tessellated, so finding the proportion of darker tiles in this region will answer the question. The top left-hand corner of this region is a 3 × 3 square that has $3 + 2(\frac{1}{2}) = 4$ darker tiles. So $\frac{4}{9}$ of the total area will be made of darker tiles.

左上角的6 × 6正方形区域是镶嵌的，所以找出这个区域中深色瓷砖的比例就能回答问题。这个区域的左上角是一个3 × 3正方形，其中有 $3 + 2(\frac{1}{2}) = 4$ 个深色瓷砖。所以总面积的 $\frac{4}{9}$ 是深色瓷砖。

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