From a point within an equilateral triangle, perpendiculars drawn to the three sides are 6 cm, 7 cm and 8 cm respectively, the length of the side of the triangle is:

Solution (By Examveda Team)

$$\eqalign{ & {\text{Length of side}} = \frac{2}{{\sqrt 3 }}\left( {{P_1} + {P_2} + {P_3}} \right) \cr & = \frac{2}{{\sqrt 3 }}\left( {6 + 7 + 8} \right) \cr & = \frac{2}{{\sqrt 3 }} \times 21 \cr & = \frac{{42}}{{\sqrt 3 }} \times \frac{{\sqrt 3 }}{{\sqrt 3 }} \cr & = \frac{{42\sqrt 3 }}{3} \cr & = 14\sqrt 3 {\text{ cm}} \cr} $$