Tiling with rectangles

A tiling with rectangles is a tiling which uses rectangles as its parts. The domino tilings are tilings with rectangles of $1 × 2$ side ratio. The tilings with straight polyominoes of shapes such as $1 × 3$, $1 × 4$ and tilings with polyominoes of shapes such as $2 × 3$ fall also into this category.

Congruent rectangles
Some tiling of rectangles include:

Tilings with non-congruent rectangles
The smallest square that can be cut into (m × n) rectangles, such that all m and n are different integers, is the 11 × 11 square, and the tiling uses five rectangles.

The smallest rectangle that can be cut into (m × n) rectangles, such that all m and n are different integers, is the 9 × 13 rectangle, and the tiling uses five rectangles.