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In the diagram below, we have DE = 3EC and AB = DC = 20. Find the length of FG.

 

 Jun 2, 2021
 #1
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Note that if DE = 3EC

 

Then    3EC  + EC  =  20

4EC =  20

EC =  20 / 4    =  5

So  DE =  3 * 5  =  15

 

Note that riangles DFE  and  BFA  are similar 

 

And  DE / BA   =    15/20  = 3/4

 

Which also means  that    DF / BF  =   3/4

 

So    BF / BD    =  BF / (BF + FD) =  4  / (4 + 3)  =     4/7

 

And  triangle  FGB is similar to triangle DCB

 

So

 

FG / DC     =     BF / BD

 

FG /  20  =   (4/7)

 

FG  =  20 (4/7)   =   80/7

 

cool cool cool

 Jun 2, 2021

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