Question

Given the altitude of an equilateral triangle is 12 cm, find the exact perimeter of the triangle

Answer 1

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 =
`8 √(3) cm;`
The exact perimeter of the triangle is 3x;

`24 √(3) cm.`