Real Life Math Application (Perimeter Problem)?

So, say you have a 2 x 4 room for simplicity's sake. Your job is to create a grid for the room. There are two ways to do this. In both methods, the outer perimeter is the same, but the tricky part comes when you are doing the inside. Say you stagger the grid every .5 units. You can make the grid run the length or the width of the room (Not criss-cross). What I want to know is, why when you run it one way, there is a difference in length of material needed than the second way? And why is that difference always equal to the difference in dimensions? For example, in the 2 x 4 room, one method will require 2 units less grid.