[tex]\displaystyle\\
\text{De\!\,finitie:}\\
\boxed{_\text{\bf Mediana uneste varful triunghiului cu mijlocul laturii opuse.}}\\\\
a)\\
BC_1= \sqrt{8}~cm=2\sqrt{2}~cm ~\Longrightarrow~AB=2\times 2\sqrt{2}=4 \sqrt{2}~cm \\\\
BA_1=\sqrt{18}~cm=3\sqrt{2}~cm~\Longrightarrow~BC=2\times 3\sqrt{2}=6 \sqrt{2}~cm\\\\
AB_1 = \frac{5\sqrt{2}}{2}~cm~\Longrightarrow~AC=2\times \frac{5\sqrt{2}}{2}=5 \sqrt{2}~cm\\\\
P=AB+BC+AC=4 \sqrt{2}+6 \sqrt{2}+5 \sqrt{2}= \boxed{\bf 15\sqrt{2}~cm}
[/tex]