If l is the median of an equilateral triangle the what is its area ........

Quantitative Aptitude (CDS) Mensuration 2D

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If l is the median of an equilateral triangle, the what is its area?

$\frac{\sqrt{3}}{3}l^{2}$

$\frac{\sqrt{3}}{2}l^{2}$

$\sqrt{3}l^{2}$

2l²

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Explanation:

$Area \: of\: equilateral\: triange =\frac{\sqrt(3)}{4}a^{2}$
In an equilateral triangle, the height and the median are considered to be of same length. Hence we can say that, Height of an equilateral triangle is equal to Median of the same equilateral triangle.
According to question median of the triangle = l = $\frac {\sqrt{3}}{2}a$
$a= \frac{2l}{\sqrt{3}}$
$=> area\: of\: equilateral \: triangle = \frac{\sqrt{3}}{4}(\frac{2l}{\sqrt{3}})^{2}= \frac{\sqrt{3}l^{2}}{3}$