Answer: Side = 2 cm, perimeter = 6 cm
For an equilateral triangle of side a, the altitude bisects the base and makes a \(30^\circ\)–\(60^\circ\)–\(90^\circ\) triangle, so
\[\text{height} = \frac{\sqrt{3}}{2} a\] \[\frac{\sqrt{3}}{2} a = \sqrt{3} \Rightarrow a = 2\ \text{cm}\] \[\text{Perimeter} = 3 \times 2 = 6\ \text{cm}\]