The question of the geometric sequence

Question

Let $h_a$, $h_b$,$h_c$ are heights of a triangle with $h_b^2=h_a.h_c$ and $q = \frac{{{h_b}}}{{{h_a}}}$.

Which of the numbers 2 and 3 and 1.9 and 1.5 can be value of $q$?

Answer 1

Let's see. The sides of a triangle are inversely proportional to its heights, so they too form a geometric sequence with the same ratio. Also, the sides are subject to the triangle inequality: $a