Partitioning a rectangle into small perimeter rectangles

We show that the way to partition a unit square into k2+s rectangles, for s=1 or s=-1, so as to minimize the largest perimeter of the rectangles, is to have k-1 rows of k identical rectangles and one row of k+s identical rectangles, with all rectangles having the same perimeter. We also consider the analogous problem for partitioning a rectangle into n rectangles and describe some possible approaches to it. © 1992.