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A rectangle with sides of length (2n-1) and (2m-1) units is divided into squares of unit length. Find the number of rectangles which can be formed wit the sides of odd length.

A rectangle with sides of length (2n-1) and (2m-1) units is divided into squares of unit length. Find the number of rectangles which can be formed wit the sides of odd length.

Grade:11

1 Answers

Arun
25763 Points
3 years ago
There are 2m vertical (numbered 1, 2, …., 2m) and 2n horizontal lines . To form the required rectangle we must select two horizontal lines, one even numbered and one odd and one even and similarly two vertical lines. The number of rectangles is then mC1.mC1.nC1.nC1.=(m^2)*(n^2)

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