Find the length of the side and perimeter of an equilateral triangle whose height is √3 cm.

Let BD be height of the triangle.
Since ABC is equilateral, BD is a perpendicular bisector.
AD = a/2
BD = √3 [given height = √3]
AB = a
Applying Pythagoras theorem in ABD
AB² = AD²+BD²
a² = (a/2)²+(√3)²
a² = (a²/4)+3
(3/4)a² = 3
a² = 4
a = 2
Hence length of side of equilateral triangle is 2 cm.
Perimeter = 3×2 = 6 [Perimeter of equilateral triangle = 3×side]
Hence perimeter of equilateral triangle is 6 cm.