Question

find the height of an equilateral triangle, side=2a​

Answer 1

An equilateral triangle is a triangle in which all three sides are equal and each internal angle is 60°.

So if one side is 2a , then the other sides should also be equal to 2a .

Lets name the sides A, B, C.

A=B=C=2a

Now in an equilateral triangle, the height from any of its side is from its mid-point(it is the perpendicular bisector of that side)

Lets consider the side as C.

So by Pythagoras Theorem

h =√{ A2 − (C2)2 }

h = √{ (2a)2−(2a2)2 }

h = √ { 4a2−a2 }

h = √{ 3a2 }

h = a√3

So the height is a√3 for any given value of a

You can find the height by multiplying the value of a by 1.732(approx decimal value of √3)