Parallelogram inside Triangle!

Calculus Level 5

Given a acute angled triangle \(ABC\) with sides \(a=10,b=11,c=12 \) . \(D,E,F\) are interior points of the sides \(BC,CA,AB\) respectively so that \(AFDE\) is a parallelogram. Let the maximum area of the parallelogram be \(X\).

Then \(\lfloor 100X \rfloor \) is -

\(a,b,c\) are standard notations denoting sides of triangle.

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