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

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 (A) 2 / √15 (B) 3 / √5 (C) 4 / √5 (D) none of these

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/477f1079b32a8bce20736fc0148ce698-.png" /> The given lines are y+2 x=1 and y+2 x=2. The distance between the lines is (2-1) / √5=1 / √5. The side length of the triangle is (1/√5) operatornamecosec 60°=(2/√15)

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 $PQR$ is an equilateral triangle. The length of the side of the triangle is

$2/ 15$

$3/ 5$

$4/ 5$

none of these

The given lines are $y + 2 x = 1$ and $y + 2 x = 2$ . The distance between the lines is $(2 - 1) / 5 = 1/ 5$ .
The side length of the triangle is
$\frac{1}{5} cosec 6 0^{\circ} = \frac{2}{15}$

Q. P is a 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

2/15​

3/5​

4/5​