To determine which of the given lengths \(s\) would result in a rational perimeter for a square, we start with the formula for the perimeter \(P\) of a square:
\[ P = 4s \]
The perimeter is rational if \(s\) is rational. Let's evaluate each of the given options for \(s\):
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\(\sqrt{20}\): \[ \sqrt{20} = \sqrt{4 \times 5} = 2\sqrt{5} \] This is an irrational number.
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\(3\sqrt{9}\): \[ 3\sqrt{9} = 3 \times 3 = 9 \] This is a rational number.
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\(\sqrt{12}\): \[ \sqrt{12} = \sqrt{4 \times 3} = 2\sqrt{3} \] This is an irrational number.
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\(2\sqrt{5}\): This is already stated as \(s\) being \(2\sqrt{5}\), which is an irrational number.
Thus, among the given options, the only length that results in a rational perimeter when the side length \(s\) is \(3\sqrt{9} = 9\).
Therefore, the correct answer is: \(3\sqrt{9}\)