The height of an equilateral triangle is 33√3. Find the perimeter of this triangle.

Let’s denote our triangle ABC with base AB and height CK = 33√3.
The height in an equilateral triangle is both the median and the bisector.
Consider a triangle BKC. Let BK = x, then BC = 2x.
By the Pythagorean theorem we have:
BC ^ 2 = CK ^ 2 + BK ^ 2
4x ^ 2 = 3267 + x ^ 2
3x ^ 2 = 3267
x ^ 2 = 1089
x = 33
Side of triangle 66, perimeter 66 * 3 = 198.
Answer: the perimeter of the triangle 198.