In an equilateral triangle, all sides are equal in length. If the perimeter is 48, then each side length can be calculated as follows:
\[ \text{Side length} = \frac{\text{Perimeter}}{3} = \frac{48}{3} = 16 \]
Now, to find the length of the perpendicular bisector of any side, we can use the properties of an equilateral triangle and a bit of geometry. The perpendicular bisector will extend from the midpoint of the side to the opposite vertex.
In an equilateral triangle, the length of the perpendicular bisector can be derived using the formula:
\[ \text{Perpendicular bisector length} = \frac{\sqrt{3}}{2} \cdot \text{Side length} \]
Substituting the side length we calculated:
\[ \text{Perpendicular bisector length} = \frac{\sqrt{3}}{2} \cdot 16 = 8\sqrt{3} \]
Thus, the length of the perpendicular bisector of any of its sides is:
\[ 8\sqrt{3} \]
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