Let the triangle be ABC with AD as its altitude. Then, D is the midpoint of BC. In right-angled triangle ABD, we have:
AB2 = AD2 + DB2
⟹ AD2 = AB2 − DB2 = 4a2 − a2 (∵ BD = 1/2 BC)
= 3a2
AD = √3a
Hence, the length of the altitude of an equilateral triangle of side 2a cm is √3a cm.