Question

The number of non - congruent rectangles that can be found on a chess board is

Answer 1

We need non congruent rectangles means every rectangle should have unique pair of length and breadth, i.e. no two rectangles should have same length and breadth.
Number of rectangles having length as $1$ unit will be like
$(1,1),(1,2),...(1,8)$
Total $8$ rectangles.
Now, number of rectangles having length as $2$ units will be like
$(2,2),(2,3),....(2,8)$
Total $7$ rectangles.
Similarly number of rectangles having length as $3$ units will be like
$(3,3),(3,4),....(3,8)$
Total $6$ rectangles.
Number of rectangles having length as $8$ units will be
$(8,8)$, only $1$ rectangle.
Total rectangles will be $8+7+6+....+1=36$