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Points $F$, $E$, and $D$ are on the sides $\overline{AB}$, $\overline{AC}$, and $\overline{BC}$, respectively, of right $\triangle ABC$ such that $AFDE$ is a square. If $AB = 12$ and $AC = 8$, then what is $AF$?

 

I heard latex works on this site so I'm going to try it out.

 

Thanks!

 #1
avatar+18309 
0

Deleted this answer....See Chris' answer !     Thanks CPhil !

 Feb 8, 2018
edited by Guest  Feb 8, 2018
edited by Guest  Feb 8, 2018
 #2
avatar+101252 
+1

Draw AD.....

 

This bisects  angle   BAC

 

And an apex angle that is bisected sets up the following relationship :

 

AB / AC  =   DB / DC

 

12/8  = DB /DC   (1)

 

But   DF  is parallel to base  CA....so  it splits sides  AB and AC proportionally

 

Thus

 

DB /DC  =  FB / FA

 

Subbing  (1)....we have that

 

12/8  = FB / FA

 

Thus.....side BA  is split into 20 equal parts......and  FA  =  AF  is 8 of these

 

So.... AF  =

 

(8/20) (12)  =  96/20  =   4.8

 

 

cool cool cool

 Feb 8, 2018
 #3
avatar+1438 
+2

Thanks you guys! Super helpful!


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