## Task 1 - 311211

Four villages form the vertices of a square with a side length of $4 \mathrm{~km}$.

Investigate whether it is possible to connect these villages with a road network of less than $11 \mathrm{~km}$ in total length.
Such a road network is possible; for example, in the coordinate system where the four villages $A, B, C, D$ have the coordinates $(0 ; 0),(4 ; 0),(4 ; 4),(0 ; 4)$, choose the points $E, F$ with the coordinates $(2 ; 1),(2 ; 3)$ and then the road network from the segments $A E, B E, E F, E C, F D$ (see figure).

Its total length, measured in $\mathrm{km}$, is $2+4 \sqrt{5}$, which is less than $11 \mathrm{~km}$ because $\sqrt{5}<\frac{9}{4}$. Adapted from $[5]$