Question

Um triângulo equilátero tem área igual a 8 raiz quadrada de 3 cm2 .qual é a medida do lado desse triângulo

Answer 1

$\mathrm{A=\dfrac{a^2\sqrt{3}}{4}\ \to\ 8\sqrt{3}=\dfrac{a^2\sqrt{3}}{4}}\\\\ \mathrm{4.8\sqrt{3}=a^2\sqrt{3}\ \to\ a^2=\dfrac{32\sqrt{3}}{\sqrt{3}}\ \to\ a^2=32}\\\\ \mathrm{a=\sqrt{32}\ \to\ a=\sqrt{2^2.2^2.2}\ \to\ a=2.2\sqrt{2}}\\\\ \mathrm{\boxed{\mathbf{a=4\sqrt{2}\ cm}}}$