Question

Find the number of rectangle which can be formed with sides of odd length, if it is given that a rectangle with sides 2m – 1 and 2n – 1 is divided into squares of unit length.
A) m2n2
B) mn(m + 1)(n + 1)
C) 4m + n – 1
D) None of these

Answer 1

Answer:

m2n2

Step-by-step explanation:

There are 2m vertical (numbered 1, 2, …., 2m) and 2n horizontal lines (numbered 1, 2, ….2n).

            To form the required rectangle we must select two horizontal lines, one even numbered and one odd numbered

            and similarly two vertical lines. The number of rectangles is then mC1.mC1.nC1.nC1.=m2n2.

            Alternate solution:

            Number of rectangles possible is (1 + 3 + 5 + …. +(2m – 1)) (1 + 3 + 5 + …. + (2n – 1)) = m2n2.