If each side of a rectangle is increased by 13%, then its area will increase by:

Let the length of the rectangle = $$l$$

Breadth of the rectangle = $$b$$

Area of the rectangle = $$lb$$

Length of the rectangle when increased by 13% = $$\frac{113}{100}l\ $$

Breadth of the rectangle when increased by 13% = $$\frac{113}{100}b$$

New area of the rectangle = $$\frac{113}{100}l\times\frac{113}{100}b$$ = $$\frac{12769}{10000}lb$$

$$\therefore\ $$Percentage increase in area = $$\frac{\frac{12769}{10000}lb-lb}{lb}\times100=\frac{2769}{10000}\times100$$ = 27.69%

Hence, the correct answer is Option A