A certain gentleman has plenty of time at his disposal. He puts his pencil to paper one day and draws a square. He then decides to create a design, so he draws another square inside the earlier one by joining its mid points. He then draws a third square inside the second in a similar fashion. He likes the design and hence goes on making squares inside squares in this manner. The side of the first square drawn is 8 cm. What is the ratio of the sum of area to the sum of perimeter of all the squares?