Question

In triunghiul abc AB=20; BC=25; AC=30.Fie D apartine BC astfel inacat CD pe BC =2/3 si paralele DE la AB, E apartine (AC) iar DF la AC, F apartine (AB). Aflati perimetrul patrulaterului AFDE.

Answer 1

DE||AB ⇒ ΔDEC asemenea Δ BCA⇒ CD/BC=CE/AC=DE/AB
2/3=CE/30=DE/20
CE= 2*30:3=60:3=20 cm⇒ AE=30-20=10 cm
DE=2*20:3=40/3 cm

DF||AC⇒ ΔBDF asemenea ΔBCA ⇒ BF/BA=BD/BC=DF/AC
1/3=BF/20=DF/30⇒ BF=20/3⇒ AF=60/3-20/3=40/3
DF=30/3=10
P AFDE= AF+FD+DE+AE=10+10+40/3+40/3=20+80/3= 60/3+80/3=140/3 cm