(S) is the side of the smaller square and (L) is the side of the larger square; ratio of the perimeters = (4L)/(4S).

***The 4s will cancel leaving us with (L/S) -> remember that this is the answer we are looking for.When you draw the figure with the smaller square inscribed in a circle, which is inscribed in a larger square, you will see that the diagonal of the smaller square = side of the larger square (L)

***Diagonal of the smaller square = the side of the larger square.Diagonal of smaller square = S\(\sqrt{2}\)

Side of Larger Square (L) = S\(\sqrt{2}\) -> Plug this into the equation (L/S)

(S\(\sqrt{2}\))/(S) -> the S cancels leaving us with

\(\sqrt{2}\) as the answer (C)
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