Question

一个正方形地板由全等的正方形瓷砖铺成。如果位于两条对角线上的瓷砖总数是 $37$ ，那么铺满地板共有多少块瓷砖？

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?

$148$

$324$

$361$

$1296$

$1369$

答案：C

知识点：对角线完全平方数

难度评级：1140

视频讲解：

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文字解答：

两条对角线共有 $37$ 块瓷砖，表示每条对角线上有 $19$ 块瓷砖，因为中间有一块重叠。每行瓷砖数等于一条对角线上的瓷砖数，所以总瓷砖数为 $19^2 = 361$ 。

所以正确答案是 C。

$37$ tiles on both diagonals imply that there are $19$ tiles on each diagonal, since one tile overlaps in the middle. The total number of tiles would then be $19^2 = 361$ since the number of tiles in each row is equal to the number of tiles in one diagonal.

Thus, C is the correct answer.

2017 AMC 8 第 11 题

答案：C

难度评级：1140

视频讲解：

文字解答：

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