Question

Calcule o comprimento da circunferência circunscrita a um quadrado de área 12m2

Answer 1

$\text{Lado do quadrado:}\\\\A=l^2\\\\12m^2=l^2\\\\l=\sqrt{12m^2}\\\\l=2\sqrt3m\\\\\\\text{Raio:}\\\\r^2+r^2=l^2\\\\2r^2=l^2\\\\r=\sqrt{\dfrac{l^2}{2}}\\\\\\r=\sqrt{\dfrac{(2\sqrt3m)^2}{2}}\\\\\\r=\sqrt{\dfrac{12m^2}{2}}\\\\\\r=\sqrt{6m^2}\\\\r=\sqrt{6}m\\\\\\\text{Comprimento:}\\\\C=2\cdot\pi\cdot{r}\\\\C=2\cdot\pi{(\sqrt{6}m)}\\\\\boxed{C=2\pi\sqrt{6}m}$