Question

If an equilateral triangle, having centroid at the origin, has a side along the line, $x+y=2$, then the area (in sq.units) of this triangle is:

• A. $6$
• B. $6\sqrt{3}$
• C. $\frac{9}{2}\sqrt{3}$
• D. $3\sqrt{6}$

Answer 1

The correct option is B $6\sqrt{3}$

$OM=\frac{|2|}{\sqrt{2}}=\sqrt{2}$ $\Rightarrow AM=3\sqrt{2}$

In $\Delta ABM$

$A{B}^2=A{M}^2+B{M}^2$

$\Rightarrow a^2=(3\sqrt{2}{)}^2+{\left(\frac{a}{2}\right)}^2$

$\Rightarrow \frac{3a^2}{4}=18$

$\Rightarrow a^2=24$

$\therefore area=\frac{\sqrt{3}}{4}{a}^2=\frac{\sqrt{3}}{4}\times 24=6\sqrt{3}$