Question

A point θ 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 ∆ is-

• A.
• B.
• C. P
• D. None of these

Answer 1

Answer: (C)

P

Answer 2

Given a = b = c

Area of triangle ABC =$\frac { \sqrt { 3 } } { 4 }$a² = area of triangle ABQ + area of triangle BQC + area of triangle CQA

$\frac { \sqrt { 3 } } { 4 }$ a² =$\frac { 1 } { 2 }$ax + $\frac { 1 } { 2 }$ by + $\frac { 1 } { 2 }$ cz

$\frac { \sqrt { 3 } } { 2 }$ a = (x + y + z) = P