Task 2. The ratio of the areas of the sides of a cuboid is 2:3:5. Determine the ratio of the lengths of the edges of the cuboid.
Solution. Let $a, b$ and $c$ be the lengths of the edges of the cuboid. From the condition of the problem, we have $a b: b c: c a=2: 3: 5$, that is, $\frac{a b}{2}=\frac{b c}{3}=\frac{c a}{5}$. According to this, $\frac{a}{2}=\frac{c}{3}$ and $\frac{b}{3}=\frac{a}{5}$. However, then $\frac{a}{10}=\frac{c}{15}$ and $\frac{b}{6}=\frac{a}{10}$. According to this, $\frac{a}{10}=\frac{b}{6}=\frac{c}{15}$. Therefore, $a: b: c=10: 6: 15$.