Determine the area of a rectangle if you know that the width is equal to $\frac{2}{3}$ of its length and the perimeter measures $148 \mathrm{~cm}$.

(M. Volfová)
If we divide the length of the rectangle into three equal parts, then the width of this rectangle corresponds to two of these three parts. The perimeter then corresponds to 10 such parts, because $3+2+3+2=10$. We know the perimeter of the rectangle, which is $148 \mathrm{~cm}$. This means that one of the mentioned parts has a length of $148: 10=14.8(\mathrm{~cm})$. Now we can easily determine the dimensions of the given rectangle and its area:

- length (3 parts): $a=3 \cdot 14.8=44.4(\mathrm{~cm})$,
- width (2 parts): $b=2 \cdot 14.8=29.6(\mathrm{~cm})$,
- area: $S=a \cdot b=44.4 \cdot 29.6=1314.24\left(\mathrm{~cm}^{2}\right)$.

Evaluation. 2 points for the insight that the perimeter of the rectangle is formed by ten parts, and its justification; 1 point for calculating the length of one part; 1 point each for the dimensions of the rectangle and the final 1 point for the area.