2002 AMC 8 第 11 题

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所有题目均经美国数学协会(MAA)官方合法授权使用。

11.

一列正方形由相同的正方形瓷砖组成。每个正方形的边长比前一个正方形多一块瓷砖长度。图中显示了前三个正方形。第七个正方形比第六个正方形多需要多少块瓷砖?

A sequence of squares is made of identical square tiles. The edge of each square is one tile length longer than the edge of the previous square. The first three squares are shown. How many more tiles does the seventh square require than the sixth?

1111

1212

1313

1414

1515

答案:C
知识点:完全平方数找规律
难度评级:1060
解答:

第六个和第七个正方形的边长分别是 6677 个瓷砖长度。

它们分别使用 62=366^2=3672=497^2=49 块瓷砖,所以第七个正方形多需要 4936=1349-36=13 块瓷砖。

所以正确答案是 C

The sixth and seventh squares have side lengths 66 and 77 tile lengths.

They use 62=366^2=36 and 72=497^2=49 tiles, respectively, so the seventh square requires 4936=1349-36=13 more tiles.

Thus, C is the correct answer.

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