# If the altitude of an equilateral triangle is #8sqrt3#, what is the perimeter of the triangle?

##### 1 Answer

The altitude of an equilateral triangle is the perpendicular line from a vertex to the opposite side.

This always forms a 30, 60, 90 triangle with the two triangles that form. (Try to prove this for "fun" Hint: HL = HL and CPCTC)

What do we know about 30-60-90 triangles? We know the relationship between angles and side lengths!

Since the altitude is opposite the 60 degree angle, the altitude is equal to

Therefore, we can set

Clearly,

Since the side opposite the 30 degree angle is x, the other leg length would be

Finally, we know that the hypotenuse is 2x, so the length would be

We are trying to find the perimeter; we know that one side is 16.

Alas, it is an equilateral triangle, so all of the sides are length 16.

So we just add the lengths up,