Question

in triunghiul ABC consideram punctul E€(AB) si construim EF||BC,F€(AC).Daca AE=6 cm,EB=9 cm si AC=20 cm aflati AF.....please

Answer 1

                A          
               /* 
             /       * 
       E  /_______*  F
         /                     * 
       /______________*
     B                             C

a) Daca AC=20 cm EB=9 cm si FC=6CM . calculati AF AE si AB
AF = AC - FC = 20 - 6 = 14cm
AE / EB = AF / FC
AE = EB(AF / FC) = 9(14 / 6) = (9*14) / 6 = 21
AB = AE + EB = 21 + 9 = 30 cm

b)  Daca FC=4  AB=8 si AC=12 cm calculati AE BE si AF
AF = AC - FC = 12 - 4 = 8 cm
AE / AB = AF / AC
AE = AB (AF / AC) = 8(8 / 12) = 8*2/3 = 16/3 cm
BE = 8 - 16/3 = (24 - 16) / 3 = 8 / 3  cm

c) Daca AE=12 cm, EB=18 cm si AF=10 cm calculati AB FC si AC
AB = AE + EB = 12 + 18= 30 cm
AE / EB = AF / FC
FC = (EB * AF) / AE = (18 * 10) / 12 = 15 cm
AC = AF + FC = 10 + 15 = 25 cm

d) Daca AB=16 cm EB=6 cm si FC=18 cm calculati AE AF si AC
AE = AB - EB = 16 - 6 = 10 cm
AE / EB = AF / FC
AF = FC(AE / EB) = 18 (10 / 6) = 30 cm
AC = AF + FC = 30 + 18 = 48 cm

E bine?