[tex]\displaystyle \\
6) \\
\texttt{Se da: }\\
A_{\Delta echilaterat} = 9 \sqrt{3} ~cm^2 \\ \\
\texttt{Se cere: } \\
a) ~l = ? \\
b)~ R = ? \\
c) ~ r = ? \\ \\
\texttt{Rezolvare: } \\ \\
a) \\
A_{\Delta echilaterat} = \frac{l^2 \sqrt{3}}{4} = 9 \sqrt{3} ~cm^2 \\ \\
\Longrightarrow ~~l^2 = \frac{4 \times 9 \sqrt{3}}{\sqrt{3}} =4 \times 9 =36 \\ \\
l = \sqrt{36} = \boxed{6~cm} \\\\\\
b) \\ \\
h = \frac{ l\sqrt{3} }{2} = \frac{ 6\sqrt{3} }{2} = \boxed{3\sqrt{3} ~cm}[/tex]
[tex]\displaystyle \\ \\
R = \frac{2}{3}\times h = \frac{2\times 3\sqrt{3} }{3}= \boxed{2\sqrt{3} ~cm } \\ \\
c) \\ \\
r = a_3 = \frac{1}{3}\times h = \frac{1\times 3\sqrt{3} }{3}= \boxed{\sqrt{3} ~cm } [/tex]
