If the increase in the side of square is 6 % , then the approximate percentage increase in its area ......

Step-by-step solution

Let side of square =x Given, percentage change in side =6 % d x x 100=6 % We have, A=x^2 Differentiate w.r.to ' x ' d A d x =2 x d A=2 x d x Dividing by x^2 on both sides aligned d A x^2 & =2 x d x x^2 d A A & =2 d x x aligned [ A=x^2 ] Now, multiply by 100 d A A 100=2 ( d x x 100 ) aligned Percentage change in Area & =2 6 % [from Eq. (i)] & =12 % aligned Hence, option (2) is correct.