+1450 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!
+36916 Deleted this answer....See Chris' answer ! Thanks CPhil !
+128631 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
