Puzzle-1 (CSAT-2011)

Consider the figure given below and answer the question that follows:

A square is divided into four rectangles as shown above. The lengths of the sides of rectangles are natural numbers. The areas of two rectangles are indicated in the figure. What is the length of each side of the square?

(a)10           (b) 11     (c) 15          

(d) cannot be determined as the given details are insufficient   
Solution follows here:

Solution:
The possible sides of the rectangle with area 15 are 1,15 and 3,5
The possible sides of the rectangle with area 48 are 1,48 & 2,24 & 3,16 & 4,12 & 6,8
For getting equal sides for the outer square, the only possibilities are 3,5 for first rectangle and 6,8 for the second. These dimensions suite the requirement. (observe that 3+8=5+6 = 11, which is the side of the outer square)
Answer (b)