Three concentric circles have radii 3,4 , and 5 . An equilateral triangle with one vertex on each circle has side length s. The largest possible area of the triangle can be written as a+\frac{b}{c} \sqrt{d}, where a, b, c, and d are positive integers, b and c are relatively prime, and d is not divisible by the square of any prime. Find a+b+c+d.