This earlier post asks, among other things, whether the plane can be tiled with mutually non-congruent rectangles all of which have same length of diagonal: Tiling the plane with mutually non-congruent equal area rectangles
Question: Given an integer n, how does one characterize those rectangles that can be cut into n mutually non-congruent rectangles all of which have same length of diagonal? What are the values of n (if they exist) for which a square can be given such a partition?
Note: https://nandacumar.blogspot.com/2016/06/non-congruent-tiling-ongoing-story.html records the question of tiling the plane with rectangles for which both dimensions are unique (no constraint on the diagonal length) but with some upper bound on the length to width ratio.
