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:

Answer: Option C

Solution

Answer: Option C

Solution:

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