Area, Perimeter and Quadrilateral

Geometry Level 4

This problem is from the OMO.

Let \(ABCD\) be a quadrilateral with \(AD = 20\) and \(BC = 13\). The area of \(ABC\) is \(338\) and the area of \(DBC\) is \(212\). Compute the smallest possible perimeter of \(ABCD\).

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