12. 如图19-3,在$□ ABCD$中,$DE ⊥ AB$于点$E$,$DF ⊥ BC$于点$F$,$□ ABCD$的周长是$36$,$DE=4\sqrt{3}$,$DF=5\sqrt{3}$,求$AD$,$CD$的长.

图19-3

12.$\because\ \ S_{□ABCD}=DE·AB=DF·BC,\therefore\ \ 4\sqrt{3}·AB=5\sqrt{3}·BC,\therefore\ \ AB:BC=5:4$.
$\therefore\ \ AB=\frac{5}{9}×18=10,BC=\frac{4}{9}×18=8.\therefore\ \ AD=8,CD=10$.