P is a point on the line y+2x=1, and Q a...

`P` is a point on the line `y+2x=1,` and Q and R 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 (a)`2/(sqrt(5))` (b) `3/(sqrt(5))` (c) `4/(sqrt(5))` (d) none of these

`2//sqrt(15)`

`3//sqrt(5)`

`4//sqrt(5)`

none of these

Text Solution

Verified by Experts

The correct Answer is:

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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