+0  
 
0
3
1
avatar+818 

Can you solve this?

 

In triangle $ABC$, points $D$ and $F$ are on $\overline{AB},$ and $E$ is on $\overline{AC}$ such that $\overline{DE}\parallel \overline{BC}$ and $\overline{EF}\parallel \overline{CD}$. If $AF = 1$ and $DF = 2$, then what is $BD$?

 Apr 2, 2024
 #1
avatar+128399 
+1

                               A

                          1

                     F

                 2

           D                                     E

 

 

B                                                             C

 

FE patallel to DC so triangles AFE  and ADC  are similar

AF / FE  = AD / DC

1 / FE  = 3 / DC

FE = (1/3)DC

3FE = DC

 

FE parallel to DC   and DE parallel to BC  so triangle FDE  is similar to triangle DBC

FD / FE = BD /  DC

FD / FE = BD /  (3FE)

FD = BD /  3

3FD = BD

3*2 = BD =  6 

 

cool cool cool

 Apr 2, 2024

0 Online Users