Question

A rectangle with sides $2m-1$ and $2n-1$ divided into squares of unit length. The number of rectangle with can be formed with sides of odd length is

• A. $m^2{n}^2$
• B. $mn(m+1)(n+1)$
• C. $4^{m+n-1}$
• D. None of these

Answer 1

The correct option is A $m^2{n}^2$

There are $2m$ vertical and $2n$ horizental lines. To form the required rectangle, we must select $2$ horizental lines. One even no. and one odd and one even. and similarly two vertical lines. The number of rectangle is then, $m{c}_1\times m{c}_1\times n{c}_1\times n{c}_1=m^2{n}^2.$