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Interesting Parallelogram

A point XX is drawn on the diagonal of a parallelogram ABCDABCD. The lines parallel to the sides through XX are constructed, and quadrilaterals PP and QQ are formed, as shown in the diagram.

Given that QQ has base 1212 and perpendicular height 44 and that the area of ABCDABCD is 200200, find the sum of all possible values of the base of PP.

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