A rectangle is divided by m lines parallel to one pair of opposite sides and n lines parallel to the other pair.

Question

 

The question is: A rectangle is divided by m lines parallel to one pair of opposite sides and n lines parallel to the other pair. How many rectangles are there in the figure obtained?

 

So far, I have only got (l/m -1) is the no. of vertical rectangle segments if length of rectangle be l 

and I also got that w/n +1 where this denotes the number of horizontal segments. where w is the width of the rectangle.

I tried to multiply these two together, but I didn't get the correct answer. The correct answer is 

[(m+2)(m+1) (n+1) (n+2)]/4 how? 

Answer 1

Each m line makes m + 1 rectangles

Each n line makes n + 1 rectangles

Together they make (m + 1)(n + 1) rectangles

 

Make several drawings with 1, 2, and 3 lines for each of m and n.