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Aria unui triunghi echilateral este
[tex]4 \sqrt{3} cm^{2} [/tex]
Perimetrul triunghiului este de ... cm.





Răspuns :

[tex]A = 4 \sqrt{3} \: {cm}^{2} [/tex]

[tex]A = \frac{ {l}^{2} \sqrt{3} }{4} [/tex]

[tex] \frac{ {l}^{2} \sqrt{3} }{4} = 4 \sqrt{3} [/tex]

[tex] {l}^{2} \sqrt{3} = 4 \times 4 \sqrt{3} [/tex]

[tex] {l}^{2} \sqrt{3} = 16 \sqrt{3} \: | \div \sqrt{3} [/tex]

[tex] {l}^{2} = 16[/tex]

[tex]l = \pm\sqrt{16}= \pm4 = > l = 4 \: cm[/tex]

[tex]P = 3l = 3 \times 4 = 12 \: cm[/tex]

[tex]\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[/tex]