# If the length of the meadian ofan equilateraltriangle is x cmthen find its area (in cm 2)?

$We\;are\;given\;median\;which\;is\;altitude\; (or\;height)\;in\;case\;of\; equilateral\;triangle\\* Length\;of\;median=x\;cm\\* Let\;suppose\;side\;of\;the\;triangle=a\;cm\\* Now,\;In\;\triangle ABD\\* BD=CD=\frac{a}{2}\\* AB^2=BD^2+AD^2\\* a^2=\frac{a^2}{4}+x^2\\* \frac{3a^2}{4}=x^2\\*\Rightarrow a=\sqrt{\frac{4x^2}{3}}=\frac{2x}{\sqrt3}\\* Area\;of\;triangle=\frac{1}{2}\times base\times height\\* Area\;of\;triangle=\frac{1}{2}\times a \times x=\frac{1}{2}\times \frac{2x}{\sqrt3}\times x =\frac{x^2}{\sqrt{3}}\;cm^2\\* So,\;area\;of\;traingle\;is\;\frac{x^2}{\sqrt{3}}\;cm^2$

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