Question

In triunghiul ABC,E apartine lui AB,F apartine lui AC.Daca EF||BC si:
a)AB=27 cm,AE=15 cm,FC=16 cm sa se afle EB,AF,AC.
b)AB=35 cm,AE=20 cm si AF=8 cm sa se afle FC,AC si EB!!!!
VA ROG MULT+COROANA!!!!

Answer 1

a) AB= AE+ EB=> EB= AB- AE => EB= 27- 15=> EB= 12 cm
EF|| BC=> triunghiul AEF asemenea triunghiul ABC
AE/ EB= AF/FC= EF/ BC=> 15/12= AF/16= EF/BC
15/12= AF/16 => AF= 16×15/12=> AF= 20 cm
AC= AF+ FC=> AC= 20+ 16=> AC= 36cm

b) AB= AE+ EB=> EB= AB- AE=> EB= 35- 20=> EB= 15cm
EF|| BC=> triunghiul AEF asemenea triunghiul ABC
AE/EB= AF/ FC= EF/ BC=> 20/15= 8/FC= EF/BC
20/15= 8/FC=> FC= 15×8/20=> FC= 6cm
AC= AF+ FC=> AC= 8+6=> AC=14cm