Special Right Triangles

Question

The altitude of an equilateral triangle is 10. What is the length of each side?

I understand that this problem creates two 30-60-90 triangles, and also understand the relations:

base =x hypotenuse= 2x long leg= x sq 3

Though, I am unsure how to proceed.

Answer 1

The altitude of the equilateral triangle is the side opposite the 60° angle of a 30-60-90 triangle.

So, longer leg = √3 x = 10. x = 10/√3

Hypotenuse = one side of the equilateral triangle = 2x = 20/√3 = 20√3 / 3.