AMC8 2017

AMC8 2017 · Q11

AMC8 2017 · Q11. It mainly tests Basic counting (rules of product/sum), Area & perimeter.

A square-shaped floor is covered with congruent square tiles. If the total number of tiles that lie on the two diagonals is 37, how many tiles cover the floor?

一个正方形地板上铺满了相同大小的正方形瓷砖。位于两条对角线上的瓷砖总数为37，问地板上有多少块瓷砖？

(A) 148 148

(B) 324 324

(D) 1296 1296

(E) 1369 1369

Answer

Correct choice: (C)

正确答案：（C）

Solution

Answer (C): If the total number of tiles in the two diagonals is 37, there are 19 tiles in each diagonal (with one tile appearing in both diagonals). The number of tiles on a diagonal is equal to the number of tiles on a side. Therefore, the square floor is covered by $19 \times 19 = 361$ square tiles.

答案 (C)：如果两条对角线上的瓷砖总数是 37，那么每条对角线上有 19 块瓷砖（其中有一块同时位于两条对角线上）。一条对角线上的瓷砖数等于一条边上的瓷砖数。因此，这个正方形地面共铺有 $19 \times 19 = 361$ 块正方形瓷砖。

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