Math, asked by jessicajoseph519, 9 months ago

If the area of equilateral triangle is 16 √ 3 cm^2 square then the perimeter of the is

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Answered by yashaswini3679

Answer:

$perimeter = 24cm$

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Answered by Mihir1001

$\huge{\underline{\mathfrak{\textcolor{blue}{Answer :}}}}$

$\huge\boxed{\fcolorbox{red}{#ffdfff}{24 cm}}$

$\LARGE{\underline{\mathrm{\textcolor{red}{Step-by-step \: \: explanation :}}}}$

$\LARGE{\underline{\mathtt{\textcolor{violet}{Given :-}}}}$

$area( \triangle abc) = 16 \sqrt{3} {cm}^{2}$

$\LARGE{\underline{\mathtt{\textcolor{green}{To \: \: find :-}}}}$

$perimeter( \triangle abc)$

$\LARGE{\underline{\mathtt{\textcolor{teal}{Concept \: \: used :-}}}}$

Equilateral triangle

$\LARGE{\underline{\mathtt{\textcolor{blue}{Solution :-}}}}$

let a be the side of the equilateral triangle ABC.

$\therefore \: ,$ A/Q,

$\longmapsto \frac{ \sqrt{3} }{4} {a}^{2} = 16 \sqrt{3}$

$\implies {a}^{2} = \frac{16 \sqrt{3} }{ \sqrt{3} } \times 4$

$\implies {a}^{2} = 64 \times \frac{ \sqrt{3} }{ \sqrt{3} }$

$\implies a = \sqrt{64 \times 1}$

$\implies a = \sqrt{ {(8)}^{2} }$

$\implies a = 8 \: cm$

Hence,

perimeter of the equilateral triangle ABC

$= 3a$

$= 3 \times 8 \: cm$

$= 24 \: cm$

$\LARGE{\underline{\mathtt{\textcolor{magenta}{Conclusion :-}}}}$

perimeter ( Δ ABC ) = 24 cm

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