question_answer

A point Q is selected at random inside the equilateral triangle. If sum of lengths of perpendicular dropped on sides from Q is P, then length of altitude of \[\Delta \] is-

A) \[\frac{P}{2}\]

B) \[\frac{P}{3}\]

C) P                     

D) None of these

Correct Answer: C

Solution :

Given a =b=c

Area of triangle\[ABC=\frac{\sqrt{3}}{4}{{a}^{2}}=\] area of triangle ABQ +area of triangle BQC + area to triangle CQA

\[\frac{\sqrt{3}}{4}{{a}^{2}}=\frac{1}{2}\,\,ax+\frac{1}{2}\,\,by+\frac{1}{2}\,\,cz\]

\[\frac{\sqrt{3}}{4}a=(x+y+z)=P\]