Question

the area of an equilateral triangle is 400 root 3 sq m. find its perimeter

Answer 1

This must be your answer

Answer 2

$Let \: side \:of \:an \: equilateral \: triangle = a\:m$

$\boxed { \pink { Area \:of \: equilateral \: triangle (A)= \frac{\sqrt{3}}{4} a^{2}}}$

$A = 400\sqrt{3} \: (given)$

$\implies \frac{\sqrt{3}}{4} a^{2} = 400\sqrt{3} \:$

$\implies a^{2} = 400\sqrt{3}\times \frac{4}{\sqrt{3}}$

$\implies a^{2} = 400 \times 4$

$\implies a^{2} = 1600$

$\implies a = \sqrt{40^{2}}$

$\implies a = 40 \:m$

$Now, Perimeter \:of \:the \\ equilateral \: triangle= 3a \\= 3 \times 40 \: m \\= 120 \:m$

Therefore.,

$\red { Perimeter \:of \:the \: equilateral \: triangle} \green {= 120 \:m }$

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