Squared length triangle inequalities

Geometry Level 2

A triangle has side lengths \(x,\) \(x^2,\) and \(\frac{1}{2}.\) Which of the following intervals describes all the values that \(x\) can take?

\[\left(\frac{-1+\sqrt{3}}{2},\frac{1+\sqrt{3}}{2}\right)\] \[\left[\frac{1}{2},1\right]\] \[\left(\frac{-1+\sqrt{3}}{2},\frac{1}{2}\right] \cup \left[1,\frac{1+\sqrt{3}}{2}\right)\] \[\left(\frac{-1+\sqrt{3}}{2},\infty\right)\] \[\left(0,\frac{1+\sqrt{3}}{2}\right)\]