Given that the perimeter of an equilateral triangle is 48, we can find the length of each side.
Since the triangle is equilateral, all three sides are equal in length. Therefore, if we denote the length of one side as \( s \), we have:
\[ 3s = 48 \]
Solving for \( s \):
\[ s = \frac{48}{3} = 16 \]
Now, we need to calculate the length of the perpendicular bisector of one of the sides of the triangle.
In an equilateral triangle, the perpendicular bisector of a side not only bisects the side but also serves as the height of the triangle from the vertex opposite that side. The formula for the height \( h \) of an equilateral triangle can be derived using the Pythagorean theorem. The height can be expressed in terms of the side length \( s \) as follows:
\[ h = \frac{\sqrt{3}}{2} s \]
Substituting \( s = 16 \):
\[ h = \frac{\sqrt{3}}{2} \times 16 = 8\sqrt{3} \]
Therefore, the length of the perpendicular bisector of any of its sides is \( 8\sqrt{3} \).
Among the available options, \( 8\sqrt{3} \) would match the third response (though it does not seem explicitly listed).
Thus, the answer is:
8√3
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