7.2. One side of the rectangle (width) was increased by $10 \%$, and the other (length) - by $20 \%$. a) By what percentage is the area of the new rectangle larger than the area of the original? b) Find the ratio of the sides of the original rectangle, if it is known that the perimeter of the new rectangle is $18 \%$ larger than the perimeter of the original.
Answer. a) by $32 \%$; b) $1: 4$. Solution. a) Let $a$ and $b$ be the sides of the original rectangle. Then the sides of the new rectangle are $1.1 a$ and $1.2 b$, and its area $S=1.1 a \cdot 1.2 b=1.32 a b$, which is $132 \%$ of the area of the original rectangle. Thus, the area has increased by $32 \%$. b) From the condition of the problem, we get the equality $2(1.1 a+1.2 b)=2(1.18(a+b))$, from which we obtain $0.02 b=0.08 a$. Therefore, the ratio of the sides is $\frac{a}{b}=\frac{0.02}{0.08}=\frac{1}{4}$.