A rectangle that is inscribed in a larger rectangle (with one vertex on each side) is called unstuck if it is possible to rotate (however slightly) the smaller rectangle about its center within the confines of the larger. Of all the rectangles that can be inscribed unstuck in a 6 by 8 rectangle, the smallest perimeter has the form , for a positive integer . Find .
This problem is copyrighted by the American Mathematics Competitions.
Instructions for entering answers:
For questions or comments, please email firstname.lastname@example.org.