Question

In paralelogramul ABCD,cu AB=35cm si BC=18 cm,consideram punctele E∈(CD) si F∈(DA),astfel incat DE=20cm si DF=10 cm ,EFintersectat cu AB ={M},EF intersectat cu BC={N} si se stie ca Perimetrul ΔBMN=110cm .Calculati:

a)AM

b)CN

c)MN.

Am mare nevoie de ajutoor.

Answer 1

DF=10 cm⇒ AF=18-10=8 cm
DE=20 cm⇒ EC=35-20=15cm

DE||AM⇒TFA⇒ ΔDFE~ΔAFM⇒   DF/AF = EF/MF = DE/AM
CN||DF⇒TFA⇒ ΔDEF~ΔCEN⇒   DE/EC = FE/EN= DF/CN

10/8= EF/MF =20/AM ⇒ MF= 8EF/10 = 4EF/5
 AM=20*8:10 = 16cm

20/15= EF/EN = 10/CN ⇒ EN=15EF/20
CN=15*10:20=15/2=7,5 cm

P BMN = BC+CN+MN+AM+AB
110 = 18+7,5 +MN+16+35
110-76,5= MN
MN=33,5cm