Problem 1. In a square with an area of $16 \mathrm{dm}^{2}$, two parallel sides are extended, resulting in a rectangle with an area of $28 \mathrm{dm}^{2}$. Determine the sides of the rectangle.
Solution. From the formula for the area of a square $P=a^{2}$, we get $a^{2}=16 d m^{2}$, so $a=4 d m$. One side of the rectangle is $a=4 d m$, so if we denote the side obtained by the extension as $b$, we get $a b=28 d m^{2}$, from which we find $4 b=28$, i.e., $b=7 d m$.