area of triangel using sine rule : .
for your case (equilateral triangle), and
now you have what you need to find the perimeter
Let "s" be the length of one side of the equilateral triangle. Drop a line from one vertex to the middle of the opposite side. It can be shown that this line is also perpendicular to the opposite side, dividing the equilateral triangle into two right triangles that have hypotenuse of length s and one leg of length s/2.
Taking "x" to be the length of the altitude to the equilateral triangle, which is the other leg of the right triangles, by the Pythagorean theorem, so and .
Now, the area of the equilateral triangle is "1/2 base times height" or . Set that equal to and solve for s.
Then, of course, the perimeter is 3s.