Equilateral triangle problem...?

Question

I need to find the shortest distance from each side of the triangle (the sum of the distances from a certain point needs to be the shortest)!!

Answer 1

As I understand the question, you want to find an interior point in the equilateral triangle such that the sum of the distances from each side is a minimum. And to know what that minimum is.

That point where distance is at a minimum is the center of the triangle.

Let

s = length of one side of the triangle
h = height of triangle

h = [(√3)/2]s

The distance from one side to the center point is (1/3)h. There are three such identical distances - one from each side. So the combined minimum distance is:

3(1/3)h = h = [(√3)/2]s

Answer 2

2/3 the distance from an angle to the opposite side, but this only works for equilateral triangles.

Answer 3

It will be the point of intersection of the perpindicular bisectors.
The distance is s√3 /4 from each side where s is the length of a side.
The total distance is 3s√3 /4

Answer 4

distance from midpoint to midpoint of each sides are shortest distance between two sides of equalateral triangle