Question

Pe laturile triunghiului abc se considera punctele M si N incluse in (AB),N inclus ( AC),astfel incat MN paralel cu BC .DAca AB= 9cm ,AM =3cm si NC =4cm,calculati MB , AN si AC.

Answer 1

           
$MN\;||\;BC \\ M\; \epsilon\;AB \\ N\; \epsilon\;AC \\ AB=9\;cm \\AM=3\;cm \\ =>MB = AB - AM = 9 - 3 = \boxed{6\;cm} \\ NC=4\;cm \\ \text{Aplicam Thales} \\ \\ \frac{AM}{MB}= \frac{AN}{NC} \\ \\ =>AN = \frac{AM*NC}{MB} = \frac{3*4}{6}=\frac{12}{6} =\boxed{2\;cm} \\ \\ =>AC=AN+NC=2+4=\boxed{6\;cm}$