Question

Aria unui triunghi echilateral este
$4 \sqrt{3} cm^{2}$
Perimetrul triunghiului este de ... cm.



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Answer 1

$A = 4 \sqrt{3} \: {cm}^{2}$

$A = \frac{ {l}^{2} \sqrt{3} }{4}$

$\frac{ {l}^{2} \sqrt{3} }{4} = 4 \sqrt{3}$

${l}^{2} \sqrt{3} = 4 \times 4 \sqrt{3}$

${l}^{2} \sqrt{3} = 16 \sqrt{3} \: | \div \sqrt{3}$

${l}^{2} = 16$

$l = \pm\sqrt{16}= \pm4 = > l = 4 \: cm$

$P = 3l = 3 \times 4 = 12 \: cm$

Answer 2

$\it \mathcal{A}= \dfrac{ \ell ^2 \sqrt 3}{4}=4\sqrt3 \Rightarrow \ell^2=4\sqrt3\cdot\dfrac{4}{\sqrt3} \Rightarrow \ell^2 = 4^2 \Rightarrow  \ell = 4\ cm\\ \\ \mathcal{P}=3\cdot\ell = 3\cdot4=12\ cm$