Question

In triunghiul ABC, MN paralel cu BC. M apartine AB,N apartine AC.
AM = 4 CM
MB=X-1
AN=6 CM
NC=X+1.
Aflati latura AB,AC.

Answer 1

conditie  x - 1 > 0       ;  x >1 
MN  II BC   ⇒ Δ  AMN ≈ Δ ABC 
AM / MB = AN  /  NC 
4 /  ( x -1) = 6  / ( x + 1) 
4· ( x +1) = 6·( x -1) 
4x + 4 = 6x - 6 
4 + 6 = 6x - 4x             ;    10 = 2x 
x = 5
AB =  AM + MB= 4cm + ( 5 -1) cm = 8 cm 
AC = AN + NC = 6cm + ( 5 + 1) cm  =  12 cm