The perpendicular distances from a point inside the equilateral triangle to the sides of the triangle are 7 cm, 10 cm and 13 cm. Find the  perimeter of the triangle is.

\(60\sqrt {3}\)

ΔABC is equilateral with sides "a".

P₁ = 7 cm

P₂ = 10 cm

P₃ = 13 cm

In this condition the formula to find the length of sides is:

a = \(\frac{2}{\sqrt{3}}(P_1+P_2+P_3)\)

a = \(\frac{2}{\sqrt{3}}(7+10+13)\)

a = \(\frac{2}{\sqrt{3}}×30= 2 × 10\sqrt{3}\) = 20\sqrt{3}\)

Perimeter = 3a = 3 × \(20\sqrt{3}= 60 \sqrt{3}\)