1997 AIME Problem 15

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.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.