4. It is necessary to connect four lamps located at the vertices of a square with a side length of 4 meters into one electrical network. Will 11 meters of wire be enough for this? (In other words, does there exist a connected graph containing the vertices of a square with a side length of 4, the sum of the lengths of whose edges does not exceed 11?)
Solution. Yes, enough. If connected as shown in the figure, $A E+B E+C F+$ $D F+E F=4 \cdot \frac{4}{\sqrt{3}}+4-\frac{4}{\sqrt{3}}=4+4 \sqrt{3}<11$.

![](https://cdn.mathpix.com/cropped/2024_05_06_55568ab07d9541f503efg-2.jpg?height=580&width=597&top_left_y=207&top_left_x=661)