To find the perimeter of a square, we can use the formula:
\[ P = 4s \]
where \( s \) is the side length of the square.
Given the side length \( s = 3\sqrt{32} \), we can calculate the perimeter:
\[ P = 4 \times (3\sqrt{32}) \]
Calculating that gives:
\[ P = 12\sqrt{32} \]
Now, we can simplify \( \sqrt{32} \):
\[ \sqrt{32} = \sqrt{16 \times 2} = \sqrt{16} \times \sqrt{2} = 4\sqrt{2} \]
Substituting this back into the expression for the perimeter:
\[ P = 12\sqrt{32} = 12 \times 4\sqrt{2} = 48\sqrt{2} \]
So the final answer for the perimeter of the square is:
\[ 48\sqrt{2} \]
Looking at your provided options, it seems like the answers do not match directly. However, if you just needed to confirm the perimeter based on the initial calculations, it would be \( 12\sqrt{32} \) prior to simplification.
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