Question

The vertex of an equilateral triangle is $(2,-1)$ and the equation of its base is $x+2y=1$ , the length of its sides is:

• A. $2/\sqrt{15}$
• B. $4/3\sqrt{3}$
• C. $1/\sqrt{5}$
• D. $4/\sqrt{15}$

Answer 1

Answer: (A)

In equilateral triangle all sides of a triangle are equal.
Given equation of $BC$ is $x+2y=1$
The perpendicular distance from a point $A(2,-1)$ is
$AD=\frac{|2+2(-1)-1|}{\sqrt{1+4}}$
$=\frac{|-1|}{\sqrt{5}}=\frac{1}{\sqrt{5}}$
In $\Delta ABD$,
$\sin 60^{\circ }=\frac{AD}{AB}$
$\Rightarrow AB=\frac{1}{\sqrt{5}}\times \frac{2}{\sqrt{3}}$
$=\frac{2}{\sqrt{15}}$
In equilateral triangle, median of a triangle is the mid poin.t of base.