A certain rectangular plot is almost square, as its width and length measure integers that differ exactly by one unit of measurement. The area of this plot, in square units, is a four-digit number, with the thousands and hundreds digits being the same, as well as the tens and units digits. What are the possible dimensions of this plot?
The area is a number of the form $a a b b$, where $a$ and $b$ represent digits, therefore

$$
a a b b=1100 a+11 b=11(100 a+b)
$$

Let $x$ be the width of the land. Then $x(x+1)=11(100 a+b)$, and we deduce that $x$ or $x+1$ is a multiple of 11. Searching for multiples of 11 that satisfy the obtained condition is quite laborious, so to simplify, we will establish which values $x$ can have by finding its minimum and maximum values.

- Minimum: the smallest possible area is 1111, so $x(x+1)=1111$ and $x>32$.
- Maximum: the largest possible area is 9999, so $x(x+1)=9999$ and $x<100$.

Now we test all $x$ between 32 and 100 such that $x$ or $x+1$ is a multiple of 11 and that $x(x+1)$ is of the form $a a b b$. We have only twelve options, as follows.

$$
\begin{aligned}
& 33 \times 34=1122,43 \times 44=1892,44 \times 45=1980,54 \times 55=2970 \\
& 55 \times 56=2970,65 \times 66=4290,66 \times 67=4422,76 \times 77=5852 \\
& 77 \times 78=6006,87 \times 88=7656,88 \times 89=7832,99 \times 100=9900
\end{aligned}
$$

We find three possibilities for the dimensions of the land, namely, $33 \times 34, 66 \times 67$ or $99 \times 100$ meters.