The height of an equilateral triangle is 96√3. Find its perimeter

AB = BC = AC (because the triangle is equilateral)
The perimeter is: P = AB + BC + CA = 3AC
AH – height, by the property of an equilateral triangle, it is also a median and a bisector.
Therefore, BH = CH = BC / 2 = AC / 2
By the Pythagorean theorem:
AC2 = AH2 + CH2
AC2 = AH2 + (AC / 2) ^ 2
AC2-AC2 / 4 = (96√3) ^ 2
3 * AC ^ 2/4 = 96 ^ 2 * 3
AC2 / 4 = 96 ^ 2
AC2 = (2 * 96) ^ 2
AC = 2 * 96 = 192
P = 3AC = 3 * 192 = 576
Answer: P = 576