Question

The height of an equilateral triangle is 15 units. How long is one of its sides?

Answer 1

Its side is `17.32` units long.

Explanation:

Let us study the following diagram, in which `a` is the side of the equilateral triangle.

Let perpendicular from vertex divides base in two equal parts and its height be `h`. Now, using Pythagoras Theorem

`a^2=(a/2)^2+h^2` or

`h^2=a^2-a^2/4`

or `h^2=(3a^2)/4`

and `h=a/2sqrt3`

Now in given case height is `15` units, hence `a/2sqrt3=15`

or `a=(15xx2)/sqrt3=(15xx2)xxsqrt3/3=10sqrt3=17.32` units