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how many rectangles are there in this figure........ please get me the answer very soon as possible

how many rectangles are there in this figure........
please get me the answer very soon as possible

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Grade:Select Grade

1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
7 years ago
Hello student,
Please find the answer to your question below
Ans: There are 70 pure rectangles, exclusive of squares in a 4 x 4 grid.
i) In a 4 x 4 grid, there are 5 parallel lines across and 5 parallel lines vertical.
To form a parallelogram we need any 2 from either set.
The selection of them is: C(5,2) x C(5,2) = 10 x 10 = 100
[This 100 inclusive of pure rectangles and squares]
ii) The number of squares:
Taking full panel, 1 x 1 = 1
Taking any 3 lines from across as well vertical, we can form 2 from either direction
==> 2 x 2 = 4 squares.
Taking any 2 lines in either direction,
the number of squares can be formed = 3 x 3 = 9
Finally 4X4 = 16 squares
So total number of squares = 1 + 4 + 9 + 16 = 30
Thus number of pure rectangles = 100 - 30 = 70

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