Question

An equilateral triangle has an altitude of 15m. What is the perimeter of the triangle?

Answer 1

`30sqrt3=51.9615` meters

Explanation:

In an equilateral triangle, all sides are equal and all angles are `60` degrees. This means that if you cut the triangle in half by the altitude(also the height in an equilateral triangle), you get `2` `30-60-90` triangles(those are the angle measures). These triangles have the relationship:

The 15 meter height is the `xsqrt3` side. To find x, divide by `sqrt3`.

`15/sqrt3*sqrt3 => (15sqrt3)/3=5sqrt3`

`x=5sqrt3`, so `2x=10sqrt3`

That is one side of the equilateral triangle, and `10sqrt3*3=30sqrt3`.

That is the perimeter.