Answers

The Brainliest Answer!
2015-10-19T17:05:48+05:30

This Is a Certified Answer

×
Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
I believe there is some typing mistake some where... 
I think that:  you should mention that:         AF : FE = 3 : 2 
then it is simpler..   

         Let  AF = 3 x  and  FE = 2 x

Draw a perpendicular from F on to AB to meet that at G.  Use similar triangles principles.

 EC / EF  = FG / FA
   EC / 2x  = 12 / 3x           =>  EC  = 8 cm

So :   BE = 12 + 8 = 20 cm        and  AB = 20 cm.
  So  AE = 20√2  cm

FE =  AE * 2/5  = 8√2 cm
==================================

In case  it is not a mistake and it is only AF : FC =  3 : 2  then,

FG = BC = 12 cm
AG = AB - BG =  AB - FC =  20 - 2 x  cm

Pythagoras theorem in triangle AFG,  we have:
       9 x²  = 12² + (20 - 2x)²
  =>  x² + 16 x - 108.8 = 0
 =>  x = √172.8  - 8  cm    ≈ 5.145  cm

AF = 3x   ≈  15.435  cm
AG = 20 - 2x =  9.71  cm
FC = 2x = 10.29 cm

 FE   ≈  16.36 cm
2 5 2
click on thanks button above pls;; select best answer
Thank you sir