[tex]\displaystyle\\
A_\Delta = \frac{l^2 \sqrt{3} }{4} \\\\
121\sqrt{3} = \frac{l^2 \sqrt{3} }{4}\\\\
\frac{l^2 \sqrt{3} }{4}=121\sqrt{3} ~~~~~\Big|\cdot 4\\\\
l^2 \sqrt{3} = 4\cdot 121\sqrt{3}~~~~~\Big|:\sqrt{3}\\\\
l^2 = 4\cdot 121\\\\
l = \sqrt{4\cdot 121} =\sqrt{2^2\cdot 11^2} =2\cdot 11\\\\
\boxed{l \bf = 22}[/tex]
