Problem:
A large square region is paved with n2 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 sd​ for this larger value of n?
Answer Choices:
A. 256​
B. 41​
C. 259​
D. 167​
E. 169​
Solution:
First, since n=24, there are n2=242=576 squares. Since we aren't given the area of the large square and only the ratios within it, we can define the area to be 1. The total area of the gray region is given by 10064​=(54​)2, so the area for each square is
