Question

In triunghiul ABC;D apartine lui Ab si E lui Bc.astfel incat DE paralel pe AC a) Daca Bd=16cm Ab=28 cm si EC=9cm calculati AD,BE,si BC b)Daca Ad=6cm Ab= 16cm si Ec=18cm calculati Bd Be si Bc c) daca Ab=35 cm si Bd=20 cm si be=8 cm calculati AD,EC,BC d) daca ab= 24cm eb=18. Cm si fc =12cm calculati bd,be,bc.

Answer 1

a)
AD=AB-BD=28-16=12 cm
BD/AB=BE/(BE+EC)
notam BE=x
16/28=x/(x+9)
28x=16x+144
12x=144
BE=x=12
BC=12+9=21

b)
BD=AB-AD=16-6=10 cm
BD/AB=BE/(BE+EC)
notam BE=x
10/16=x/(x+18)
16x=10x+180
6x=180
BE=x=30
BC=30+18=48

c)
AD=AB-BD=35-20=15 cm
BD/AB=BE/(BE+EC)
notam EC=x
20/35=8/(x+8)
20x+160=280
20x=120
EC=x=6
BC=8+6=14

d)
BD/AB=BE/(BE+EC)
notam BD=x
x/24=18/12
12x=432
BD=x=36
BC=18+12=30