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The distance between two parallel lines ...

The distance between two parallel lines is unity. A point P lies between the lines at a distance a from one of them. Find the length of a side of an equilateral triangle PQR, vertex Q of which lies on one of the parallel lines and vertex R lies on the other line.

A

`(2)/(3) sqrt(d^(2)+d+1)`

B

`2sqrt((d^(2)-d+1)/(3))`

C

`2sqrt(d^(2)-d+1)`

D

`sqrt(d^(2)-d+1)`

Text Solution

Verified by Experts

The correct Answer is:
B
From figure ltbr. `x cos (theta+30^(@))=d`
and `x sin theta=1-d`
Dividing `sqrt(3) cot theta=(1+d)/(1-d)`
squaring Eq. ii and putting the value of `cos theta` , we get
`x^(2)=(1)/(3)(4d^(2)-4d+4)`
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