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. $\frac{4}{\sqrt{15}}$
• B. $\frac{2}{\sqrt{15}}$
• C. $\frac{4}{3\sqrt{3}}$
• D. $\frac{1}{\sqrt{15}}$

Answer 1

The correct option is B $\frac{2}{\sqrt{15}}$


Distance, $AD=\frac{|2+2(-1)-1|}{\sqrt{1^2+2^2}}=\frac{1}{\sqrt{5}}$
Let $AB=a$
In $△ABD,$
${\left(\frac{a}{2}\right)}^2+A{D}^2=a^2$
$\Rightarrow \frac{3}{4}{a}^2=\frac{1}{5}$
$\Rightarrow a=\frac{2}{\sqrt{15}}$