To find the length of the perpendicular bisector of any side of an equilateral triangle, we first need to determine the length of each side of the triangle.
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Given that the perimeter of the equilateral triangle is 48, we can calculate the length of one side: \[ \text{Length of one side} = \frac{\text{Perimeter}}{3} = \frac{48}{3} = 16. \]
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Next, we can find the height (which is also the length of the perpendicular bisector of one side) of the equilateral triangle using the formula for the height \(h\) of an equilateral triangle: \[ h = \frac{\sqrt{3}}{2} \cdot a, \] where \(a\) is the length of a side.
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Substituting the value of \(a = 16\): \[ h = \frac{\sqrt{3}}{2} \cdot 16 = 8\sqrt{3}. \]
Thus, the length of the perpendicular bisector of any of its sides is \(8\sqrt{3}\).
The correct response is: 8√3.
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