Explanation:
Consider the dissection of the given 6 x 6 square in to non-congruent rectangle with least possible areas. The only rectangle with area 1 is an 1X1 rectangle. Similarly, we get 1x2, 1x3 rectangle for areas 2, 3 units. In the case of 4 units we may have either a 1x4, rectangle or a 2 x2 square. Similarly, there can be a 1x 5 rectangle for area 5 units and 1 x 6 or 2 x 3 rectangle for 6 units. Any rectangle with area 7 units must be 1 x 7 rectangle, which is not possible since the largest side could be 6 units .And any rectangle with area 8 units must be a 2 x 4 rectangle. If there is any
which is the area of the given square. Hence if a 6 x 6 square is dissected in to 9 rectangles as stipulated in the problem, there must be two congruent rectangles.
