Question

Let the point O lies in the interior of an equilateral triangle with side lengths 2 units,each .Find the sum of the shortest distance from P to the sides of the triangle,

Answer 1

Shortest distance of a forest from long a line is $\perp r$ to the line

Hence P must be in centre

in $centre=\frac{\Delta }{5}=\frac{\frac{\sqrt{3}}{4}{a}^2}{\frac{3Q}{2}}=\frac{Q}{2\sqrt{3}}=\frac{1}{\sqrt{3}}$

Sum of shortest distance = $\frac{1}{\sqrt{3}}+\frac{1}{\sqrt{3}}+\frac{1}{\sqrt{3}}=\sqrt{3}$