Question

Triunghiul ABC are laturile AB=21cm, AC=35cm si BC=28cm.Fie D∈BC astfel incit BD/DC=2/5.Prin punctul D se duc paralelele DE la AB,E∈AC si DF la AC,F∈AB.Aflati perimetrul lui AEFD

Answer 1

DE paralel AB ⇒cf thales BD/DC=AE/EC=2/5
AE/(AE+EC)=2/7; AE/AC=2/7; AE/35=2/7; AE=2*35/7⇒
AE=10
FD paralel AC⇒ cf thales BD/DC=BF/FA=2/5
BF/(BF+FA)=2/(2+5)
BF/21=2/7
BF=6
FB=AB-FB=21-6=15
FD paralel AE si FA paralel ED⇒AEDF= paralelogram⇒FD=AE=10; AF=ED=15
PERIMETRUL=2*15+2*10=50