Question

The equation of the base of an equilateral triangle with vertex at $(2,-1)$ is $x+y-2=0$. Then find its length of sides.

Answer 1

We know the perpendicular distance of the vertex of an equilateral triangle to its base is its height.

Now for the given triangle the height is $=\left|\frac{2-1-2}{\sqrt{1^2+1^2}}\right|=\frac{1}{\sqrt{2}}$.

Let $a$ be the side of the equilateral triangle.

Then,

$\frac{\sqrt{3}}{2}\times a=\frac{1}{\sqrt{2}}$

or, $a=\sqrt{\frac{2}{3}}$.