7.2. The length of the rectangle was increased by $12 \%$, and the width - by $15 \%$. a) By what percentage is the area of the new rectangle larger than the area of the original? b) Find the ratio of the length to the width of the original rectangle, if it is known that the perimeter of the new rectangle is $13 \%$ larger than the perimeter of the original.
Answer. a) by $28.8 \%$. b) 2:1. Solution. a) Let $a$ and $b$ be the length and width of the rectangle, respectively. Then the sides of the new rectangle are $1.12 a$ and $1.15 b$, and its area $S=1.12 a \cdot 1.15 b=1.288 a b$, which is $128.8 \%$ of the area of the original rectangle. Thus, the area has increased by $28.8 \%$. b) From the problem statement, we get the equality $2(1.12 a + 1.15 b)=2(1.13(a+b))$, from which we obtain $0.02 b=0.01 a$. Therefore, $a=2 b$.