Question

The equation of the base of an equilateral triangle is $x+y-2=0$ and the vertex is $(2,-1),$ then the length of side is

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

Answer 1

The correct option is D $\sqrt{\frac{2}{3}}$

Distance of $(2,-1)$ from the line $x+y-2=0$

$d=|\frac{2-1-2}{\sqrt{2}}=\frac{1}{\sqrt{2}}|$

Let each side of equilateral $\Delta$ is a

So, $a\cos {30}^{\circ }=\frac{1}{\sqrt{2}}$

$a=\frac{2}{\sqrt{6}}=\sqrt{\frac{2}{3}}$

So, length of side is $\sqrt{\frac{2}{3}}$