2019 Mock AMC 10B Problems/Problem 5
The intersection of the medians in a triangle is the centroid, which splits each median into a 2:1 ratio. Also, in an equilateral triangle, each median divides the opposite leg into 2 equal parts, so we can find the length of each median by the Pythagorean theorem - We have a right triangle with legs 1 and 1/2, so the length of the other leg (the median) is sqrr3/2.
Let 2x be the length of PA/PB/PC, and x= the length of the other part of the median. Solving for x, we have x= sqrt3/6, and 2x= sqrt3/3. 3(sqrt3)/3= sqrt3. The answer is (D).