If an equilateral triangle has a perimeter of 96, what is the length of the perpendicular bisector of any of its sides?(1 point)
The length of the perimeter of an equilateral triangle is equal to 3 times the length of one of its side.
Let's call the length of one side of the equilateral triangle "x".
So the perimeter of the triangle is given by:
3x = 96
Divide both sides of the equation by 3:
x = 32
The length of one side of the equilateral triangle is 32.
Now, let's consider the perpendicular bisector of one of the sides of the triangle. Since the triangle is equilateral, the perpendicular bisector will also be the altitude of the triangle.
An equilateral triangle has a special property where the altitude, perpendicular bisectors, and medians are all the same length.
Therefore, the length of the perpendicular bisector of any side of the equilateral triangle will also be 32 units.