Three boys are standing on a circular boundary of a fountain. They are at equal distance from each other. If the radius of the boundary is 5 m, the shortest distance between any two boys is :
Options:
A . $$\frac{{5\sqrt 3 }}{2}m$$
B . $$5\sqrt 3 \,m$$
C . $$\frac{{15\sqrt 3 }}{2}m$$
D . $$\frac{{10\pi }}{3}m$$
Answer: Option B Let A, B and C denote the portions of the three boys Then, AB = BC = AC So, ΔABC is equilateral Let the side of ΔABC be a Then, $$\eqalign{ & \frac{a}{{\sqrt 3 }} = 5 \cr & \Rightarrow a = 5\sqrt 3 \cr} $$ ∴ Required shortest distance = $$5\sqrt 3 \,m$$
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