Task 3. The ratio of the areas of the sides of a cuboid is 2:3:5. Calculate the ratio of the edges of that cuboid.
Solution. Let $a b: b c: c a=2: 3: 5$, i.e., $\frac{a b}{2}=\frac{b c}{3}=\frac{c a}{5}$. From this, $\frac{a}{2}=\frac{c}{3}$ and $\frac{b}{3}=\frac{a}{5}$, so $\frac{a}{10}=\frac{c}{15}$ and $\frac{b}{6}=\frac{a}{10}$. Therefore, $\frac{a}{10}=\frac{b}{6}=\frac{c}{15}$, hence

$$
a: b: c=10: 6: 15
$$