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

Step-by-step solution

Number of rectangles possible is = (Number of ways to choose a horizontal side of odd length).(Number of ways to choose a vertical side of odd length) 1 + 3 + 5 + ..... + 2 m - 1 1 + 3 + 5 + ..... + 2 n - 1 = m 2 n 2