'O' is a point in the interior of an equilateral triangle. The perpendicular distance from 'O' to the sides are $\sqrt{3}$cm, $2\sqrt{3}$cm, $5\sqrt{3}$cm. The perimeter of the triangle is:

48 cm

We know that,

Height of an equilateral triangle = \(\frac{\sqrt {3}}{2}\)Side

Height of equilateral triangle = sum of perpendicular distance with point

Perimeter of an equilateral triangle = 3 × side

The perpendicular distance =  P₁ = \(\sqrt {3}\)

 P₂ = 2\(\sqrt {3}\)

 P₃ = 5\(\sqrt {3}\)

Height of equilateral triangle = (\(\sqrt {3}\) × side) × \(\frac{1}{2}\)  = P1 + P2 + P3 

= (\(\sqrt {3}\) × side) × \(\frac{1}{2}\)  = \(\sqrt {3}\) + 2\(\sqrt {3}\) + 5\(\sqrt {3}\)

= side = 8 × 2 = 16 cm

Perimeter of an equilateral triangle = 3 × side = 3 × 16 = 48 cm