4.072 The lengths of the sides of a triangle are three consecutive terms of a geometric progression. Compare the common ratio of this progression with the number 2.
Solution. Let $b, b q, b q^{2}$ be the lengths of the sides of the triangle. By the triangle inequality, $b+b q>b q^{2} \Rightarrow q^{2}-q-1<0 \Rightarrow q<\frac{1+\sqrt{5}}{2}<2$.

Answer: less than 2.