question_answer

P is point on the line \[y+2x=1,\] and Q and R are two points on the line \[3y+6x=6\]such that triangle PQR is an equilateral triangle. The length of the side of the triangle is

A) \[2/\sqrt{15}\]

B) \[3/\sqrt{5}\]

C) \[4/\sqrt{5}\]

D) None of these

Correct Answer: A

Solution :

[a] The given lines are \[y+2x=1\] and \[y+2x=2.\] The distance between the lines is \[(2-1)/\sqrt{5}=1/\sqrt{5}.\] The side length of the triangle is \[\frac{1}{\sqrt{5}}\cos ec60{}^\circ =\frac{2}{\sqrt{15}}.\]