Question

If the area of an equilateral triangle is 24√3m², then its perimeter is​

Answer 1

Question :-

If the area of an equilateral triangle is 24√3m², then its perimeter is-

Answer :-

$\rightarrow \boxed{\sf perimeter = 12 \sqrt{6} } \:$

To find :-

→ perimeter of equilateral triangle.

Formula used :-

$\star \: \sf{ area \: of \: equilateral \triangle = \frac{ \sqrt{3} }{4} {a}^{2} } \\ \sf \: here \: a \: is \: the \: side \: of \: triangle \\ \\ \star \: \sf perimeter \: of \: equilateral \triangle = 3a$

Explanation :-

given that ,

let "a" be the side of triangle .

→ area of equilateral triangle = 24√3 m²

$\implies \: \sf 24 \sqrt{3} = \frac{ \sqrt{3} }{4} {a}^{2} \\ \\ \implies \: \sf {a}^{2} = 96 \\ \: \\ \implies \: \sf a = \sqrt{96}$

hence ,

$\rightarrow \sf \: perimeter = 3a \\ \\ \rightarrow \: \sf \: perimeter = 3 \sqrt{96} \\ \\ \rightarrow \boxed{\sf perimeter = 12 \sqrt{6} }$

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