Fitting a known size rectangle to 4 point sets in 3D

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I have a point set which represents a rectangle of known size. I would like the extract the 4 corner points as accurate as possible. I did a Ransac line fit through each point set and computed the corners by intersecting the lines. But the lines may be non parallel or non perpendicular to each other and their length is arbitrary.

Given the information that I know the size and geometry of the structure, can I fit a rectangle with known size to the point set? I found this, where they fit a rectangle to a point set. How could I additionally include the size of the rectangle into the optimization?

Thanks