Smallest Area Possible

Geometry Level 4

For a rectangle \(ABCD\) with coordinates \(A = (0,0), B = (5,0)\), \(C= (5,3) , D = (0,3) \), let \(P\) denote a varable point lying between the rectangle \(ABCD\).

And we define \(d(P,L) \) as the perpendicular distance of point \(P\) from line \(L\). Suppose

\[ d(P,AB) \leq \min\left[d(P,BC), d(P,CD), d(P,AD) \right]. \]

Find the area of the region in which \(P \) lies.

Not original question. I like this and thought of sharing it with you guys.

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