To find the perimeter of a square, we use the formula:
\[ P = 4s \]
where \(s\) is the side length of the square. In this case, the side length \(s\) is given as \(2\sqrt{27}\).
First, let's simplify \(2\sqrt{27}\):
\[ \sqrt{27} = \sqrt{9 \times 3} = \sqrt{9} \times \sqrt{3} = 3\sqrt{3} \]
So, we have:
\[ 2\sqrt{27} = 2 \times 3\sqrt{3} = 6\sqrt{3} \]
Now that we have simplified the side length, we can compute the perimeter:
\[ P = 4s = 4(6\sqrt{3}) = 24\sqrt{3} \]
Therefore, the perimeter of the square is:
\[ \boxed{24\sqrt{3}} \]