11. Determine the lengths of the sides of a rectangle if their ratio and the area of the figure are known.

## Problems from the Kahun Papyrus.
11. If the sides of the rectangle are $x$ and $y$, then the problem reduces to solving the system of equations:

$$
\frac{x}{y}=\frac{m}{n} \text { and } x y=S
$$

Multiplying these equations gives:

$$
x^{2}=\frac{m}{n} \cdot S
$$