AMC 8 2020 Problem 24

AMC8 2020 年第 24

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A large square region is paved with n^2 gray square tiles, each measuring s inches on a side. A border d inches wide surrounds each tile. The figure below shows the case for n=3. When n=24, the 576 gray tiles cover 64% of the area of the large square region. What is the ratio d/s for this larger value of n?
一个大的正方形区域是用个灰色的方形瓷砖铺成的,每块的边长都是 s 英寸。每一块瓷砖周围都有一个 d 英寸宽的边框。下图显示了 n=3 的情况。当 n=24 时,576 块灰色瓷砖覆盖了大正方形面积的 64%。对于这个较大的 n 值, 的比值是多少?
AMC 8 2020 Problem 24 figure
  1. A.625\frac6{25}
  2. B.14\frac14
  3. C.925\frac9{25}
  4. D.716\frac7{16}
  5. E.916\frac9{16}

正确答案 · Correct Answer

A

解析 · Solution

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