## Task B-1.4.

A lively hedgehog is hopping through a meadow, first moving 4 meters to the east, then 2 meters southwest, and finally 4 meters to the south. How far is the hedgehog from its starting position?
## Solution.

![](https://cdn.mathpix.com/cropped/2024_05_30_bde1d6b20cdcb90302c4g-02.jpg?height=868&width=973&top_left_y=490&top_left_x=462)

For the sketch.

The angle $\measuredangle E B C=45^{\circ}$, so $|E B|=|E C|=\sqrt{2}$.

$$
\begin{aligned}
|A E| & =4-\sqrt{2},|E D|=4+\sqrt{2} \\
|A D| & =\sqrt{|A E|^{2}+|E D|^{2}}=\sqrt{(4-\sqrt{2})^{2}+(4+\sqrt{2})^{2}} \\
& =\sqrt{16-8 \sqrt{2}+2+16+8 \sqrt{2}+2}=\sqrt{36} \\
|A D| & =6 \text{ m}
\end{aligned}
$$