Question

The area of an equilateral triangle whose two vertices are (1,0) and (3,0) and third vertex lying in the first quadrant is-

• A. $\sqrt{3}/4$
• B. $\sqrt{3}/2$
• C. $\sqrt{3}$
• D. None of these

Answer 1

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

CD is perpendicular(also median) to AB$\Rightarrow D(2,0)$

In $\Delta CDB$, $\tan 60=\frac{CD}{DB}\Rightarrow \sqrt{3}=\frac{CD}{1}$

$\Rightarrow CD=\sqrt{3}$

$\Rightarrow C(2,\sqrt{3})$

Area $=\frac{1}{2}\times$ base$\times$ height

$=\frac{1}{2}\times 2\times \sqrt{3}=\sqrt{3}\Rightarrow \left(C\right)$.