Question

The equation of base of an equilateral triangle is $x+y=2$ and the vertex is $(2,-1)$. The length of side of the triangle is?

Answer 1

Let, a be the length of each side of equilateral triangle

The length of perpendicular from $(2,-1)orx+y-2=0$

$\Rightarrow p=|\frac{2-1-2}{\sqrt{1^2+1^2}}|=\frac{1}{\sqrt{2}}x+y-2=0$

Consider $\Delta ABC$

$\sin 60°=\frac{8}{a}\Rightarrow \frac{\sqrt{3}}{2}=\frac{\frac{1}{\sqrt{2}}}{a}\Rightarrow a=\frac{2}{\sqrt{3}}\times \frac{1}{\sqrt{2}}a=\frac{\sqrt{2}}{3}$

Hence the length of side of equilateral triangle is $\frac{\sqrt{2}}{3}$