Question

If $\lambda$ is the length of any edge of a regular tetrahedron, then the distance of any vertex form the opposite face is-

• A. $\frac{2}{3}{\lambda }^2$
• B. $\sqrt{\frac{2}{3}}\lambda$
• C. $\frac{\sqrt{2}}{3}\lambda$
• D. $Noneofthese$

Answer 1

The correct option is A $\frac{2}{3}{\lambda }^2$

$\begin{array}{c}In{30}^0-{60}^0-{90}^0-sideisinratio,\\ 1:\sqrt{3}:2\end{array}$

In regular tetraheron, height (h)

$\begin{array}{c}5\frac{\sqrt{2}}{3}\\ andside,s=\lambda \\ \therefore \lambda =\sqrt{\frac{2}{3}}\lambda \end{array}$