252. Find the sides of a rectangle given that its perimeter and area are numerically equal to each other, and the sides are expressed in whole numbers.
252. We have the equation $2 x+2 y=x y$. Let's represent it as $\frac{1}{x}+\frac{1}{y}=\frac{1}{2}$. Find the equal values of $x$ and $y$: $x=4, y=4$. Next, each of the positive fractions $\frac{1}{x}$ and $\frac{1}{y}$ must be less than $\frac{1}{2}$, hence, $x>2$, $y>2$. Moreover, one of these fractions, for example $\frac{1}{x}$, must be greater than half of their sum, i.e., $\frac{1}{x}>\frac{1}{4}$, thus $x<4$. Therefore, $2<x<4$, hence, $x=3, y=6$.

Answer. (4,4$),(3,6),(6,3)$.