Points F, E, D are on the sides AB, AC, and BC , respectively, of right triangle ABC such that AFDE is a square. If AB = 12 and AC = 18, then what is AF?
+128570 Note that triangles BAC and BFD are similar
Since AB = 12, let the side of the square = x = AF
Then BF = 12 - x ....and by similar triangles we have that
AB / FB = AC / DF
12 / ( 12- x) = 18 / x .....cross-multiply
12x = ( 12 - x ) 18
12x = 216 - 18x ...... add 18x to both sides
30x = 216 .......divide both sides by 30
x = 216 / 30 = 7.2 = AF
