Question

if an equilateral triangle has a perimeter of 48, what is the length of the perpendiculr bisector of any of its sides
the answer choices are 16\sqrt()3, 8\sqrt()3,8 or16
8 \sqrt()2 is not the answer

Answer 1

Let's label the length of each side of the equilateral triangle as "x". Since an equilateral triangle has three equal sides, we can set up the equation:

3x = 48

Now, let's solve for x:

x = 48 / 3
x = 16

Therefore, the length of each side of the equilateral triangle is 16.

The perpendicular bisector of any side of an equilateral triangle will pass through its centroid. The centroid divides each median in a 2:1 ratio, with the longer segment being twice as long as the shorter segment.

Therefore, the length of the perpendicular bisector is:

16 / 2 = 8

So, the length of the perpendicular bisector of any side of the equilateral triangle is 8.