How to calculate the co-ordinates of a quadrilateral knowing the side lengths

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Hi I've come across a mathematical problem, which I can't seem to solve with my limited geometry and trigonometry knowledge.

I need to draw a quadrilateral (may not be rectangle always). To draw this quadrilateral, I need to know the coordinate points of each corner. All I know is the length of all four sides and co-ordinates for top side (100,0) and (600,0).

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There is no guarantee on the orientation of the box. At any given point of time only one side can be a straight (0 degrees) or perpendicular (90 degrees) side. So the sides are not 90 degrees to each other.

Any help? This seems like it should be easy, but it is really stumping me.

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It appears that is one such quadrilateral in the first quadrant and another in the third. I scaled the sides to $10,12,6,13$.