Given Triangle, Any Side, Any Point!

Geometry Level 5

The lengths of the sides of a triangle \(ABC\) are \(4,5\) and \(6\). Take any point \(D\) on any one of the sides of the triangle and drop perpendiculars \(DP\) and \(DQ\) onto the two other sides (\(P\) and \(Q\) are on the sides). Let the minimum possible value for the length of \(PQ\) be \(L\).

If \(L\) can be expressed as \(\dfrac{A}{B}\) for positive coprime integers \(A,B\), then submit the value of \(A+B\) as your answer.

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