## Task 2 - 160822

A rectangle has side lengths $a_{1}$ and $b_{1}$.

By what percentage does the area of this rectangle change if the side $a_{1}$ is reduced by $25 \%$ and the side $b_{1}$ is increased by $20 \%$?
The area $A_{1}$ of the given rectangle is $A_{1}=a_{1} \cdot b_{1}$. It corresponds to $100 \%$.

The side reduced by $25 \%$ has the length $a_{2}$, then

$$
a_{2}=a_{1}-\frac{1}{4} a_{1}=\frac{3}{4} a_{1}
$$

The side extended by $20 \%$ has the length $b_{2}$, then accordingly $b_{2}=\frac{6}{5} b_{1}$.

Therefore, the area of the second rectangle, which has been changed in this way, is

$$
A_{2}=a_{2} \cdot b_{2}=\frac{3}{4} a_{1} \cdot \frac{6}{5} b_{1}=\frac{9}{10} A_{1}
$$

Thus, the area of the first rectangle has been reduced by $10 \%$.