Q. 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:
Jharkhand CECEJharkhand CECE 2004
Solution:
In equilateral triangle all sides of a triangle are equal.
Given equation of $B C$ is $x+2 y=1$
The perpendicular distance from a point $A(2,-1)$ is
$A D=\frac{|2+2(-1)-1|}{\sqrt{1+4}}$
$=\frac{|-1|}{\sqrt{5}}=\frac{1}{\sqrt{5}} $
In $\Delta A B D$,
$\sin 60^{\circ}=\frac{A D}{A B}$
$ \Rightarrow A B=\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.
