To find the length of the perpendicular bisector of one side of an equilateral triangle, we first need to determine the side length of the triangle.
Given that the perimeter of the equilateral triangle is 48, we can find the length of one side:
\[ \text{Side length} = \frac{\text{Perimeter}}{3} = \frac{48}{3} = 16 \]
Next, we can find the length of the perpendicular bisector of one side. For an equilateral triangle, the height (which is the same as the length of the perpendicular bisector from the opposite vertex to the midpoint of a side) can be calculated using the formula for the height \( h \) of an equilateral triangle:
\[ h = \frac{\sqrt{3}}{2} \times \text{side length} \]
Substituting in the side length:
\[ h = \frac{\sqrt{3}}{2} \times 16 = 8\sqrt{3} \]
Thus, the length of the perpendicular bisector of any of its sides is:
\[ 8\sqrt{3} \]
So the correct response is:
8√3