Question

un tetraedru are toate fetele triunghiuri echilaterale cu aria de 25 radical din 3. calculati suma muchiilor

Answer 1

Aria unui triunghi echilateral se calculeaza cu formula:

$A_3=\frac{l^2\sqrt{3}}{4}$

Inlocuind aria cu 25 radical din 3 obtinem:

$\frac{l^2\sqrt{3}}{4}=25\sqrt{3}=\ \textgreater \ l^2\sqrt{3}=100\sqrt{3}|:\sqrt{3}=\ \textgreater \ l^2=100 =\ \textgreater \ l = 10$

Tetraedrul are 6 muchii, deci suma muchiilor este:

$S_m=6*l=\ \textgreater \ S_m=6*10=\ \textgreater \ S_m=60$

Answer 2

25√3=l²√3/4 => l²=25√3*4/√3 => l²=25*4=100cm si l=10 cm. Suma muchiilor este 6*10=60 cm