Question

in triangle ABC, E is the midpoint of AC and D is the midpoint of CB. if DF is parallel to BE, find the length of side AB.

Answer 1

Is there an image?

Answer 2

us proportionalitie of sides

Answer 3

first try drawing it

Answer 4

here is the figure

Answer 5

so if D is the midpoint of CB what will be the lenght of CB ?
this is easy

Answer 6

10? i'm not sure

Answer 7

yes you are right

Answer 8

so then you know CB=10

Answer 9

then?

Answer 10

now you can writing the proportionalitie of sides

CD CB
---- = ----
FD BF

and from this you can calculi easy the BF

ok?

Answer 11

BF= 6

Answer 12

5 10
--- = ---
3 BF

cross multiplie

5*BF = 3*10

yes you are right

Answer 13

what's next after getting BF?

Answer 14

the same you can calculi CE

Answer 15

CF FD
--- = ----
CE EB

Answer 16

CE- 8 am i correct?

Answer 17

then CE= (EB*CF)/FD

Answer 18

sorry BE=6 not BF

BF not exist

Answer 19

yes CE=8

Answer 20

so E is the midpoint of AC what mean AC= ?

Answer 21

then the lenght of AC = ?

Answer 22

AC= 16

Answer 23

then AB = 10

Answer 24

is it correct?

Answer 25

how you have got AB=10 ?

Answer 26

\[\left(\begin{matrix}CE \\ AC\end{matrix}\right)= \left(\begin{matrix}FD \\ BE\end{matrix}\right)\]

Answer 27

then by pythagorean theorem..

Answer 28

ok i understand it now

you are right

Answer 29

Yaay.. thanks a lot :)

Answer 30

my pleasure

good luck