By the general triangle inequality, we must have $13>x>3$, and by obtuse general inequality we have, $39>x^2$ or $x^2>89.$ For $39>x^2,$ we have that $x \in (3,\sqrt{39})$ and for $x^2>89,$ we have that $x \in (\sqrt{89},13),$ so $x$ is in the intervals $(3, \sqrt{39}) \cup (\sqrt{89},13).$