To find the perimeter of an equilateral triangle from its area, we have to first find the length of one side, since the perimeter of an equilateral triangle is simply three times the length of one side.
The formula for the area of an equilateral triangle is √3/4 * a², where 'a' is a side of the triangle. We know from the problem that the area is 16√3 cm², so we can set up the equation 16√3 = √3/4 * a².
Solving this equation:
Step 1: Divide both sides by √3
This yields: 16 = a²/4.
Step 2: Multiply both sides by 4
This yields: a² = 64.
Step 3: Take the square root of both sides
This yields a = 8 cm.
So each side of the triangle is 8 cm long.
Finally, to find the perimeter of the triangle, we do 3*a, because all sides are equal in an equilateral triangle. This gives us:
Perimeter = 3*8 cm = 24 cm.
So, the perimeter of the given equilateral triangle is 24 cm.