First slide

Equation of line in Straight lines

Question

One vertex of an equilateral triangle is $(2, - 1)$ whose area is $\frac{1}{2 \sqrt{3}}$ .The perpendicular distance from the vertex $(2, - 1)$ to opposite side is

Moderate

A

$\sqrt{2}$
B

$\frac{1}{\sqrt{2}}$
C

$2 \sqrt{2}$
D

$3 \sqrt{2}$

Solution

$In an equilateral triangle, if h is the height of the triangle, then its area is \frac{h^{2}}{\sqrt{3}} .$
Here,
$\begin{matrix} \frac{h^{2}}{\sqrt{3}} = \frac{1}{2 \sqrt{3}} \\ h^{2} = \frac{1}{2} \\ h = \frac{1}{\sqrt{2}} \end{matrix}$
$Therefore, the distance from one vertex to the opposite side is \frac{1}{\sqrt{2}}$

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