Equilateral Triangle in a Square

Geometry Level 4

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 \(p+q+r.\)

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