Question

If an equilateral triangle has a perimeter of 48, what is the length of the perpendicular bisector of any of its sides?
A. 16√3
B. 8√3
C. 8
D. 16

Answer 1

To find the length of the perpendicular bisector of one side of an equilateral triangle, we start with the perimeter given as 48.

Since the triangle is equilateral, we can find the length of each side \( s \) as follows:

\[
s = \frac{\text{Perimeter}}{3} = \frac{48}{3} = 16
\]

Now, we need to find the length of the perpendicular bisector of one of the sides. For an equilateral triangle, the perpendicular bisector of a side also acts as the height of the triangle.

The height \( h \) of an equilateral triangle can be calculated using the formula:

\[
h = \frac{\sqrt{3}}{2} s
\]

Substituting \( s = 16 \):

\[
h = \frac{\sqrt{3}}{2} \times 16 = 8\sqrt{3}
\]

Thus, the length of the perpendicular bisector of any side of the triangle is:

\[
\boxed{8\sqrt{3}}
\]

So, the answer is **B. 8√3**.