1. Tardigrade
  2. Question
  3. Mathematics
  4. P is a point on the line y+2 x=1, and Q and R are two points on the line 3 y+6 x=6 such that triangle P Q R is an equilateral triangle. The length of the side of the triangle is

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

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

Straight Lines

Solution:

image
The given lines are $y+2 x=1$ and $y+2 x=2$. The distance between the lines is $(2-1) / \sqrt{5}=1 / \sqrt{5}$.
The side length of the triangle is
$\frac{1}{\sqrt{5}} \operatorname{cosec} 60^{\circ}=\frac{2}{\sqrt{15}}$