5 (1246). By what percentage will the area of a rectangle increase if its length is increased by $20 \%$ and its width by $10 \%$?
Solution. Let the length of the rectangle be $x$, and the width be $y$, then its area is $x y$. After increasing the length and width of the rectangle by $20 \%$ and $10 \%$ respectively, its area became $1.2 x \cdot 1.1 y = 1.32 x y$, i.e., the area of the rectangle increased by $0.32 x y$, which is $32 \%$ of $x y$.

Answer: the area of the rectangle increased by $32 \%$.