Equilateral Triangle in a Square

Geometry Level 5

The sides of rectangle ABCDABCD have lengths 1010 and 1111. An equilateral triangle is drawn so that no point of the triangle lies outside ABCDABCD. The maximum possible area of such a triangle can be written in the form pqrp\sqrt{q}-r, where p,q,p, q, and rr are positive integers, and qq is not divisible by the square of any prime number. Find p+q+r.p+q+r.

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