Since the shaded part is 1/3 of a square, you can cut a square into three parts including the shaded part and do the same for the other square.There should be five parts including the shaded part. Since the shaded part takes up one part of the five parts in the figure, the shaded part take up 1/5 of the figure.

As the unshaded parts is split into four parts, 108 can be divided into four and the answer represents one part. Since three parts including the shaded part is a square, the answer should be multiplied by four and it should give you a square number. A square number is a multiple of two same numbers. For example in this situation, 81=9x9. So 81 is a square number. As the area of the square is 81 which is made up by length times breadth. Which is 9x9 in this situation. Therefore, the length of the square is 9.