Question

if the area of equilatoral triangle is 400√3cm² . find its perimeter​

Answer 1

$\huge{ \bf{ \orange{ \mid{ \underline{ \overline{ \purple{work \: out...}}}}}}}$

$\large{ \bold{area \: of \: equilateral \: triangle}} \\ = \large{ \green{ \boxed{ \red{\frac{ \sqrt{3} }{4} \times (side) {}^{2} }}}}$

$\large{ \sf{ given \: area = 400 \sqrt{3} {cm}^{2} }} \\ \large{ \sf{ = > \frac{ \sqrt{3} }{4} \times {side}^{2} = 400 \sqrt{3} {cm}^{2} }} \\ \large{ \sf{ = > (side) {}^{2} = \frac{400 \sqrt{3} \times 4 }{ \sqrt{3} } }} \\ \large{ \sf{ = > (side) {}^{2} = 1600 \: cm {}^{2} }} \\ \large{ \sf{ = > side = 40 \: cm}}$

$\large{ \bold{perimeter \: of \: equilateral \: triangle}} \\ \large{ \red{ \boxed{ \green{ = 3 \times (side)}}}}$

$\large{ \sf{then \: perimeter = 3 \times 40 \: cm}} \\ \large{ \sf{ \red{ = 120 \: cm}}} (\blue{answer...})$

$\large{ \bold{ \red{ running \: in \: an \: never \: ending \: maze..}}}$

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Answer 2

$\Large{\underline{\underline{\mathfrak{\bf{Question}}}}}$

If the area of equilateral triangle is 400√3cm² . find its perimeter

$\Large{\underline{\underline{\mathfrak{\bf{Solution}}}}}$

$\Large{\underline{\mathfrak{\bf{\pink{Given}}}}}$

• the area of equilateral triangle is 400√3cm² .

$\Large{\underline{\mathfrak{\bf{\pink{Find}}}}}$

• Perimeter of equilateral triangle

$\Large{\underline{\underline{\mathfrak{\bf{Explanation}}}}}$

we know,

$\small\boxed{\sf{\blue{\:Area_{equilateral\:triangle}\:=\:\dfrac{\sqrt{3}(side)^2}{4}}}} \\ \\ \\ \mapsto\sf{\:400\sqrt{3}\:=\:\dfrac{\sqrt{3}(side)^2}{4}} \\ \\ \\ \mapsto\sf{\:(side)^2\:=\:\dfrac{400\times 4\times \sqrt{3}}{\sqrt{3}}} \\ \\ \\ \mapsto\sf{\:(side)^2\:=\:400\times 4} \\ \\ \\ \mapsto\sf{\:(side)^2\:=\:1600} \\ \\ \\ \mapsto\sf{\:(side)\:=\:\sqrt{1600}} \\ \\ \\ \mapsto\sf{\red{\:(side)\:=\:40\:cm}}$

We know,

Equilateral triangle have all same side ,

So, three angle of Equilateral triangle will be = 40, 40 and 40

So, Now find perimeter of Equilateral triangle

$\small\boxed{\sf{\blue{\:perimeter_{equilateral\:triangle}\:=\:Sum\:of\:all\:side}}} \\ \\ \\ \mapsto\sf{\:perimeter_{equilateral\:triangle}\:=\:40+40+40} \\ \\ \\ \mapsto\sf{\orange{\:perimeter_{equilateral\:triangle}\:=\:120\:cm\:\:\:\:\:\:\:(Ans.)}}$