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A rectangle of dimension m n´ (m and n being odd) is divided into square of unit length by drawing horizontal and vertical lines. The number of rectangles having side of odd unit length is

(A)  m2n2

(B)  ((m + 1)(n + 1)/4)2

(C)  ((m - 1)(m - 1)/2)2

(D)  (2m - 1)(2n - 1)

1 Answer

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Best answer

Correct option  (B)  ((m + 1)(n + 1)/4)2

Number of ways of selecting a side of odd length along the side of m units

 m + (m - 2) + (m - 4) + ....3 + 1 = 1/2(m + 1/2)(m + 1) = (m + 1)/5\

Similarly, number of ways of selecting a side of odd length along the side of n units = (n + 1)2/4

Hence, the total number of ways

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