If 'x' is the median (altitude) of an equilat | vedclass

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Question

(D) In an equilateral triangle,the median is the same as the altitude.Let the side of the equilateral triangle be '$a$'.The altitude (median) '$x$' is

Vedclass · Accepted Answer

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

Vedclass · Answer

(D) In an equilateral triangle,the median is the same as the altitude.Let the side of the equilateral triangle be '$a$'.The altitude (median) '$x$' is given by the formula: $x = \frac{\sqrt{3}}{2} a$.From this,we can express the side '$a$' in terms of '$x$': $a = \frac{2x}{\sqrt{3}}$.The area of an equilateral triangle is given by: $	ext{Area} = \frac{\sqrt{3}}{4} a^2$.Substituting the value of '$a$': $	ext{Area} = \frac{\sqrt{3}}{4} \left( \frac{2x}{\sqrt{3}} ight)^2$.$	ext{Area} = \frac{\sqrt{3}}{4} 	imes \frac{4x^2}{3}$.$	ext{Area} = \frac{\sqrt{3} x^2}{3} = \frac{x^2}{\sqrt{3}}$.

If '$x$' is the median (altitude) of an equilateral triangle,then its area is?

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