(Q). Find the number of non-congruent rectangles on a chess board.
Solution:-
Here 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.
Hence dimension (a, b) & (b, a) are congruent.
Number of non-congruent rectangles having length as 1 unit will be like
(1, 1) (1, 2) (1, 3), ………………….(1, 8) ⟹ total 8 rectangles
Now number of rectangles having length as 2 units will be like
(2, 2), (2, 3), (2, 4)…………….(2, 8) ⟹ total 7 rectangles
Similarly number of rectangles having length as 3 units will be like (3, 3) (3, 4) (3, 5) ………………………… (3, 8) ⟹ total 6 rectangles
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Number of rectangles having length as 8 units will be like (8, 8) ⟹ total 1 rectangle
Hence total number of rectangles
= 8 + 7 + 6 + ……….. + 1
= 36 Answer
