From the given information, we know that the two angle bisectors meet at R; and we know that the distance from each vertex to R is 8.
In a triangle, the three angle bisectors meet so that each bisector is divided into two lengths in the ratio 2:1; that makes the altitude of the triangle 8+4=12.
Then the ratio of the lengths of the altitude and side of an equilateral triangle is sqrt(3):2, so the side length of the triangle is
