一个大的正方形区域铺上了$n^2$块灰色的方砖，每块方砖的边长为$s$英寸 . 每块瓷砖周围都有一个$d$英寸宽的边 . 上图显示的是$n = 3$的情况 . 当$n = 24$时，576块灰色瓷砖覆盖了大正方形区域$64\%$的面积 . 对于这个较大的$n$值，比例 $\frac{d}{s}$ 是多少？

A. $\frac{6}{25}$

B. $\frac{1}{4}$

C. $\frac{9}{25}$

D. $\frac{7}{16}$

E. $\frac{9}{16}$

1. 2020 AMC 8 官方解析

When $n = 24$, there are $24^2 = 576$ gray tiles, each with an area of $s^2$ square inches. Together the tiles cover an area of $24^2 s^2$ square inches. Each side of the large square region spans 24 tiles plus 25 borders for a side length of $24s + 25d$ inches, giving a total area of $(24s + 25d)^2$ square inches. It is given that the gray tiles cover $64\%$ of the total area. It follows that