AMC 8 2017 Problem 11
AMC8 2017 年第 11 题
方程与不等式★★★☆☆
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?
一个正方形的地板由一些全等的方形瓷砖覆盖。若两条对角线上的瓷砖总个数是 37，那么铺这个地板总共用了多少块瓷砖？
- A.148
- B.324
- C.361
- D.1296
- E.1369
正确答案 · Correct Answer
C
解析 · Solution
Solution 1
Since the number of tiles lying on both diagonals is 37, counting one tile twice, there are tiles on each side, where x is the number of tiles on the side length of the square. This is because the number of tiles on the square's diagonal is equal to the number of tiles on the square's side length.Therefore, our answer is . and Add-On's by WrenMath
Visualize it as 4 separate diagonals connecting to one square in the middle. Each square on the diagonal corresponds to one square of horizontal/vertical distance (because it's a square). So we figure out the length of each separate diagonal, multiply by two, and then add 1. (Realize that we can just join two of the separate diagonals on opposite sides together to save some time in calculations.) Therefore, the edge length is Thus, our solution is .
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