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25 points！Please help me! A large square region is paved with n 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 d region. What is the ratio - for this larger value of n?

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Answer:

A: 6/25

Step-by-step explanation:

All area = a^2, where a=N*s+ (N-1)d + 2d

tiles area = N^2*s^2

Thus, (N*s)^2/(N*(s+d)+d)^2=0.64

Taking the root from both sizes we're get:

(N*s)/(N*(s+d)+d)=0.8 0r  5Ns=4Ns+4(Nd+4d), or d/s=N/(4(N+1)).

With N=24, d/s = 24/(4*25)===6/25

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