The altitude of an equilateral triangle forms a right triangle with half of the base and the side of the equilateral triangle opposite one of the right angles formed by the altitude and the base. So, if the sides of the equilateral triangle measure , and then half the base measures perforce, then Pythagoras tells us, given an altitude that measures 4:
Solve for the positive root to get the measure of one side of the equilateral triangle and then multiply that result by 3 to get the sum of the measures of the three sides which is the perimeter. I recommend you leave the answer in radical form since the question implies that an exact answer is required. Don't forget to rationalize your denominator.
John
Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it
