AUSTRIAN-POLISH 1988 Problem 9

For a rectangle $R$ with integral side lengths, denote by $D(a, b)$ the number of ways of covering $R$ by congruent rectangles with integral side lengths formed by a family of cuts parallel to one side of $R$ . Determine the perimeter $P$ of the rectangle $R$ for which $\frac{D(a,b)}{a+b}$ is maximal.