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!

AnonymousConfusedGuy
Feb 8, 2018

#1**0 **

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

ElectricPavlov
Feb 8, 2018

edited by
Guest
Feb 8, 2018

edited by Guest Feb 8, 2018

edited by Guest Feb 8, 2018

#2**+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

CPhill
Feb 8, 2018