Question

Fie ΔDEF cu m( <d)=90° DM⊥EF, (M∈EF)
b)DE=30cm EF=5dm aflati EM-MF-DF-DM
c)ME=1,8m  MF=320cm calculati lungimile EF-DE-DF-DM

Va multumesc anticipat! ofer coroana

Answer 1

b. in ΔDEF dreptunghic in D aplicam th Pitagora EF²=DE²+DF²⇒DF²=EF²-DE²
DF²=25dm²-9dm²=16dm²⇒ DF=4dm
(atentie la unitatile de masura!)

ΔEMD asemenea ΔEDF(au unghiuri respectiv congruente)⇒
⇒EM/ED=DM/DF=ED/EF=3/5⇒DM=3/5·DF=3/5·4=12/5⇒
⇒EM=3/5·ED=3/5·3=9/5dm=1,8dm
ΔFMD asemenea ΔFDE (au unghiuri respectiv congruente)⇒
⇒MD/ED=MF/DF=DF/EF=4/5⇒MF=4/5·DF=4/5·4=16/5=3,2dm
EM-MF-DF-DM=9/5-16/5-4-12/5=(9-16-20-12)/5=-39/5dm (nu prea stiu ce rost are sa calculezi aceasta diferenta)

c. ME=1,8m=18dm
MF=320cm=32dm
EF=ME+MF=50dm=5m
sirurile de rapoarte de la punctul b. se pastreaza
EM/ED=DM/DF=ED/EF⇒18/ED=DM/DF=ED/50⇒ED²=18·50
ED=√(18·50)=3·2·5=30 dm=3m
Th Pitagora in ΔEDF⇒DF²=EF²-ED²=25-9=16, DF=6m
AriaΔEDF=DM·EF/2=ED·DF/2⇒DM·5=3·6⇒DM=18/5m=3,6m