Question

DAU COROANA (AA1) ,(BB1) ,(CC1) sint medianele triunghiului ABC.Calculati perimetrul triunghiului ABC, daca
a)BC1= RADICAL DIN 8 CM, BA1=RADICAL DIN18 CM, AB1 = 5 RADICAL DIN2 SUPRA LUI 2 CM

Answer 1

   
[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]