The altitude of an equilateral triangle bisects one of the angles and the opposite side.
So, let a be the altitude of the triangle; we have the formula a=xsinθ, where x is the side of the triangle. Solving for x, x=a / sinθ;
a = 12 cm; θ = 60 degrees;
So, x = [tex]8 \sqrt{3} cm;[/tex]
The exact perimeter of the triangle is 3x;
[tex]24 \sqrt{3} cm.[/tex]
