31. A rectangular children's playground must meet the following requirements: the lengths of the sides must be expressed in whole numbers of meters, and the area must numerically equal the perimeter. What can be the length and width of such a playground?
31. If the width is $a$ m, and the length is $b$ m, then according to the condition we have $2 a+2 b=a b$, from which $2=b \cdot \frac{a-2}{a}$. The equality is possible when $a>2$ and under the conditions: 1) $a=b=4$; 2) $a=3 ; b=6$. Therefore, the possible sizes of the plots are: 1) $4 \times 4\left(\mathrm{M}^{2}\right)$; 2) $6 \times 3\left(\mathrm{M}^{2}\right)$.