If x is the side of the triangle then its altitude should be [tex] \frac{ \sqrt{3} }{2} x[/tex] (from the property of 30-60-90 triangle)
Altitude: x-2 (is 2 cm shorter than its side)
[tex]x-2= \frac{ \sqrt{3} }{2}x \\ \\ 2x-4= \sqrt{3}x \\ \\ (2- \sqrt{3})x=4 \\ \\ x= \frac{4}{2-\sqrt{3} }=\boxed{8+4 \sqrt{3}} [/tex]
Length of side = [tex]8+4 \sqrt{3}[/tex] cm
