Question

Fie triunghiul ABC, cu AB=24 cm, AC=32 cm si BC=48 cm, iar M apartine (AB) astfel incat MB/AM=3/5. Daca MN // BC, N apartine (AC), atunci calculati perimetrul trapezului MBCN. (si rezolvarea va rog, dau coroana)

Answer 1

MB/AM=3/5 => MB=3p , AM=5p
MB+AM=AB=24cm
=> 8p=24cm => p=3cm => MB=9cm , AM=15cm

MN||BC => AM/MB=AN/NC (T. Thales) => 3/5=AN/NC => AN=3k , NC=5k
AN+NC=AC=32cm
=> 8k=32cm => k=4cm => AN=12cm , NC=20cm

MN||BC => AM/AB=MN/BC (TFA) => 15cm/24cm=MN/48cm
=> MN=15*48/24 cm = 30cm

MB=9cm
NC=20cm
MN=30cm
BC=48cm

=> Perimetrul lui MBCN= 9+20+30+48=107 cm

Problema clasica de asemanare in triunghi
TFA = Teorema Fundamentala a Asemanarii
T. Thales = Teorema lui Thales