Question

Qual o comprimento da aresta de um cubo cuja diagonal tem 3√2 cm de comprimento?​

Answer 1

$\Large\boxed{\begin{array}{l}\underline{\rm Diagonal~do~cubo~de~aresta~\ell}\\\sf d=\ell\sqrt{3}\end{array}}$

$\Large\boxed{\begin{array}{l}\sf d=3\sqrt{2}\\\sf\ell\sqrt{3}=3\sqrt{2}\\\sf \ell=\dfrac{3\sqrt{2}}{2\sqrt{3}}\\\\\sf\ell=\dfrac{3\sqrt{2}}{2\sqrt{3}}\cdot\dfrac{\sqrt{3}}{\sqrt{3}}\\\\\sf \ell=\dfrac{3\sqrt{6}}{2\cdot(\sqrt{3})^{\diagup\!\!\!\!2}}\\\\\sf \ell=\dfrac{\diagdown\!\!\!\!3\sqrt{6}}{2\cdot\diagdown\!\!\!\!3}\\\\\sf \ell=\dfrac{\sqrt{6}}{2}~cm\end{array}}$