A rectangular plot of land with an area of $800 \mathrm{~m}^{2}$ is to be fenced along a river using $100 \mathrm{~m}$ of fencing. What are the dimensions of the plot?
Result: $a=10$ and $b=40$ (there are 2 sides of this type) or $a=20$ and $b=40$, and there are two of these. 1 point was given to those who found only one solution. A solution is incorrect if the solver tried to enclose all four sides of the plot, leading to the conclusion that the problem has no solution.

Note. We accepted the graphical or trial-and-error solution of the quadratic equation from students in lower grades, provided it was accompanied by a proper explanation.