Question

If the length of a median of an equilateral triangle is x cm, then its area is

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

Answer 1

The correct option is C

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

$\because$ The median of an equilateral triangle is the perpendicular to the base also,
$\therefore$ Let side of the triangle = a
$\therefore$ The perpendicular or altitude = $\frac{\sqrt{3}}{2}a$
$\Rightarrow \frac{\sqrt{3}}{2}a=x\Rightarrow a=\frac{2x}{\sqrt{3}}$
Now area = $\frac{\sqrt{3}}{4}(side{)}^2=\frac{\sqrt{3}}{4}\times {\left(\frac{2x}{\sqrt{3}}\right)}^2$
= $\frac{\sqrt{3}}{4}\times \frac{4x^2}{3}=\frac{x^2}{\sqrt{3}}$