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`P` is a point on the line `y+2x=1,` and `Qa n dR` two points on the line `3y+6x=6` such that triangle `P Q R` is an equilateral triangle. The length of the side of the triangle is `2/(sqrt(5))` (b) `3/(sqrt(5))` (c) `4/(sqrt(5))` (d) none of these

A

`2//sqrt(15)`

B

`3//sqrt(5)`

C

`4//sqrt(5)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
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
`(1)/(sqrt(5)) " cosec "60^(@) = (2)/(sqrt(15))`
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