Task 3. A square with an area of $36 \mathrm{~cm}^{2}$ is given. Determine the length of the rectangle which has a width of 3 cm and the same perimeter as the square.
Solution. The area of the square is $P=36 \mathrm{~cm}^{2}$, from which it follows that the side of the square is $6 \mathrm{~cm}$, and its perimeter is $L_{k}=4 \cdot 6=24 \mathrm{~cm}$. Then, if in the perimeter equation of the rectangle we substitute $L_{p}=24 \mathrm{~cm}$ and $b=3 \mathrm{~cm}$, we get $L_{p}=2 a+2 b \Rightarrow 24=2 a+2 \cdot 3$, from which it follows that $2 a=24-6 \Rightarrow 2 a=18$, that is, $a=9$ cm.