Question

Question
If an equilateral triangle has a perimeter of 48, what is the length of the perpendicular bisector of any of its sides?(1 point)
Responses

8
8

16
16

83–√
8 Start Root 3 End Root

163–√

Answer 1

In an equilateral triangle, the length of the perpendicular bisector of any of its sides can be found using the properties of the triangle.

First, we find the length of one side of the equilateral triangle. The perimeter of the triangle is given as 48, and since it has 3 equal sides, we can find the length of each side by dividing the perimeter by the number of sides:

\[
\text{Length of one side} = \frac{48}{3} = 16.
\]

Next, we can use the properties of triangles to find the length of the perpendicular bisector. The perpendicular bisector of a side in an equilateral triangle also serves as the height (altitude) of the triangle.

To calculate the altitude (h) of an equilateral triangle with side length \( s \), you can use the formula:

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

Substituting in our value for \( s \):

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

Thus, the length of the perpendicular bisector of any side of the equilateral triangle is \( 8\sqrt{3} \).

Therefore, the answer is:

**\(8\sqrt{3}\)**.