The side of an equilateral triangle is 16√3, find the median.

Let an equilateral triangle ABC be given, BD is its median (AD = DC = 16√3 / 2 = 81√3. In an equilateral triangle, all sides are equal, therefore AB = BC = AC = 16√3. The median of an equilateral triangle is its height. Therefore, the triangle ABD is rectangular with a right angle BDA. Using the Pythagorean theorem, we find the length of the median side BD (leg of the triangle ABD): AB ^ 2 = BD ^ 2 + AD ^ 2, BD ^ 2 = AB ^ 2-AD ^ 2, BD ^ 2 = (16√3) ^ 2- (8√3) ^ 2 = 3 * (16 ^ 2-8 ^ 2) = 3 * 192 = 576, BD = √576 = 24.
Answer: The median of the triangle is 24.