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

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

Let the side of equilateral $\triangle\text{ABC}$ be a $cm$ The median of equilateral triangle is its altitude drawn from $A$ to $BC$. $\big($i.e. the height of $\triangle$ over Base BC$\big)$ $\Rightarrow\text{x}=\frac{\text{a}\sqrt{3}}{2}$ [$AD$ = $x$(given)] $\Rightarrow\text{a}=\frac{2\text{x}}{\sqrt{3}}$ Area of equilateral $\triangle$ of side a $=\frac{\sqrt{3}\text{a}^2}{4}$ $=\frac{\sqrt{3}}{4}\Big(\frac{2\text{x}}{\sqrt{3}}\Big)^3$ $=\frac{\text{x}^2}{\sqrt{3}}$ Hence, correct option is $(c)$.

M.C.Q

GSEB - English Medium

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

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

STD 9
Maths
Herons Formula
RD Sharma

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