10.008. In an isosceles triangle with a lateral side equal to 4 cm, a median of the lateral side is drawn. Find the base of the triangle if the median is 3 cm.
Solution.

Using the cosine theorem, we get $\left\{\begin{array}{l}x^{2}=16+16-2 \cdot 16 \cos \alpha, \\ m^{2}=16+4-2 \cdot 8 \cos \alpha\end{array} \Rightarrow\right.$

$\Rightarrow x^{2}-2 m^{2}=-8, x^{2}=10, x=\sqrt{10}$ (Fig. 10.8).

Answer: $\sqrt{10}$ cm.