Question

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

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

Answer 1

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

Given: $x+y=2$.....(1) is the base of the equilateral triangle and $(2,-1)$ vertex.

Putting $(2,-1)$ in $eq.\left(1\right)$

We have,

$2-1\ne 2$

Since $(2,-1)$ doses not satisfy (1) this means the point is vertex opposite to the base.

Now the perpendicular distance of $(2,-1)$ from the line (1) is nothing but the height of the equilateral triangle.

So the perpendicular distance is $\frac{|-1|}{\sqrt{2}}=\frac{1}{\sqrt{2}}$.

Again height of an equilateral triangle be $=\frac{\sqrt{3}}{2}\times$ side.

Then,

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

Side $=\sqrt{\frac{2}{3}}$