The problem of decomposing a rectangle into p subrectangles of equal area minimizing maximal subrectangle perimeter is considered. Both continuous and discrete versions are addressed. For the continuous case it is proved that one of four certain nearly-regular decompositions is optimal. Moreover this solution turns out to be optimal for more general case of decomposing into ``pseudorectangles'' being cartesian products of measurable subsets of the real line. In the discrete setting one needs to decompose the \(A\times B\)-grid rectangle into p subsets of grid cells of nearly equal area while minimizing a certain analogue of perimeter - the sum of projections onto the coordinate axes. For this grid case three algorithms are proposed approximating the above continuous solution in different ways. The applications of the problem and open issues are also discussed.