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Doubt & Answer Explanation

Doubt

a rectangle with sides 2m-1 and 2n-1 is divided into squares of unit length. the number of rectangle which can be formed with sides of odd length is


ans--m2n2

Answer Explanation

Sol.
    A long horizontal side one unit can be taken in = (2m-1) ways
3 units can be taken in = (2m-3) ways
5 units can be taken in = (2m-5) ways
and so on



Therefore the number of ways of selecting a side horizontally is
(2m-1) +(2m-3) +(2m-5) +...+3+1=m2

Similarly the number of ways of selecting a side vertically is
(2n-1) +(2n-3) +(2n-5) +....+3+1=n2

Therefore total number of rectangles =m2 x n2 =m2 n2
 

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