Answer: Option C
Let the side of the original square be 'a'. Then the area of the square is a^2.When the area of the square increases by 96%, the new area becomes (1 + 0.96) times the original area, i.e., 1.96 times the original area.
New area of square = 1.96 × (a^2) = 1.96a^2
Let the side of the new square be 'b'. Then, we have:b^2 = 1.96a^2Taking the square root of both sides, we get:b = √(1.96) × a
So, the side of the new square is 1.4 times the original side.
The percentage increase in the side of the square can be calculated as follows:
Increase in side = New side - Original side= 1.4a - a= 0.4a
Percentage increase in side = (Increase in side / Original side) × 100%= (0.4a / a) × 100%= 40%
Therefore, the side of the square increases by 40% when the area of the square increases by 96%.
Some relevant definitions and formulas used in this solution are:

• A square is a quadrilateral with four equal sides and four right angles.
• The area of a square is given by the formula A = side^2, where 'side' is the length of a side of the square.
• Percentage increase = (Increase in value / Original value) × 100%
• In this problem, we used the fact that if the area of a square is increased by a certain percentage, then the side of the square will increase by the square root of that percentage. For example, if the area is increased by 25%, then the side will increase by the square root of 25%, which is 5%.