Problem 2. A square is cut into two rectangles. The sum of the perimeters of the two rectangles is $210 \mathrm{~cm}$ greater than the perimeter of the square. The area of one rectangle is four times larger than the area of the other. Calculate the perimeter of the smaller rectangle.
Solution. Since the sum of the perimeters of the rectangles is two side lengths of the square greater than the perimeter of the square, it follows that $a=210: 2=105 \mathrm{~cm}$. On the other hand, the area of the larger rectangle is four times the area of the smaller one, and both have one common side (the side of the square-

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a square), so the second side of the larger rectangle is four times the second side of the smaller one. Therefore, $x=105: 5=21 \mathrm{~cm}$ and the perimeter of the smaller rectangle is $2 \cdot(105+21)=252 \mathrm{~cm}$.