MathDB

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.

Problem Statement