Question

Un Tetraedru are toate fețele triunghiuri echilaterale cu aria de 25 radical3 cm patrați . Calculează suma muchiilor tetraedului

Answer 1

Aria tr.echilat. = L^2rad3/4 = 25rad3 =>L^2=100 =>L=10 cm
Suma=6×10=60 cm

Answer 2

$\it \mathcal{A}_{\triangle} = \dfrac{\ell^2\sqrt3}{4}=25\sqrt3|_{:\sqrt3} \Rightarrow \dfrac{\ell^2}{4} = 25 \Rightarrow \ell^2=25\cdot4\Rightarrow \ell^2=100 \Rightarrow \ell=10\ cm\\ \\Tetraedrul\ are\ 6\ muchii \Rightarrow suma\ lor\ este\ s = 6\cdot10=60\ cm$