Question

Stiind ca triunghiul ABC este asemenea cu triunghiul MNP, AB=3 cm, BC= 4 cm, AC=5cm si MN = 6 cm, aflati perimetrul triunghiului MNP.

Answer 1

∆ MNP≈ ABC
$\frac{mn}{ab} = \frac{mp}{ac} = \frac{np}{bc} \\ \frac{6}{ 3} = \frac{mp}{5} = \frac{np}{4} \\ \frac{6}{3} = \frac{mp}{5} = > mp = \frac{6 \times 5}{3} = 10 \: cm \\ \frac{6}{3} = \frac{np}{4} = > np = \frac{6 \times 4}{3} = 8 \: cm \: \\ p = mp + np + mn = 10 + 8 + 6 = 24 \: cm \:$