Question

Fie punctele E si F pe segmentul [AB] , astfel incat AE/EB = 5/11 si AF/FB = 3/5 . Valoarea raportului EF/BE este egala cu ... CU EXPLICATII VA ROG

Answer 1

A.........E.............F..........B
AE/EB=5/11      AE/AE+EB)=AE/AB=5/(5+11)=5/16   AE=5AB/16   
AF/FB=3/5        AF/(AF+FB)=AF/AB=3/(3+5)=3/8      AF=3AB/8      


EF=AF-AE=3AB/8-5AB/16=(6AB-5AB)/16=AB/16
BE=AB-AE=AB-5AB/16=(16AB-5AB)/16=11AB/16
EF/BE=(AB/16)/(11AB/16)=1/16 × 16/11=1/11


sau
A.........E.............F..........B
a=constanta
AE/EB=5/11           AE+EB=5a+11a=16a   ⇒AE=5a   EB=11a   
AF/FB=3/5=6/10    AF+FB=6a+10a=16a   ⇒AF=6a   FB=10a
     EF=AF-AE=6a-5a=a
     BE=11a   
   EF/BE=a/11a=1/11