The sides of rectangle $$ABCD$$ have lengths $$10$$ and $$11$$. An equilateral triangle is drawn so that no point of the triangle lies outside $$ABCD$$. The maximum possible area of such a triangle can be written in the form $$p\sqrt{q}-r$$, where $$p$$, $$q$$, and $$r$$ are positive integers, and $$q$$ is not divisible by the square of any prime number. Find $$p+q+r$$.

(第十五届AIME1997 第15题)