1997 AIME Problem 15

The sides of rectangle A B C D have lengths 10 and 11 . An equilateral triangle is drawn so that no point of the triangle lies outside A B C D. 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.