Bài giải:

Vì AD là tia phân giác nên ta có:

$\frac{AB}{AC}=\frac{DB}{DC}$ hay $\frac{15}{20}=\frac{DB}{DC}$

$\Rightarrow \frac{15}{20+15}=\frac{DB}{DC+DB}=\frac{DB}{BC}=\frac{DB}{25}$

$\Rightarrow DB=\frac{25.15}{20+15}=10\frac{5}{7}$cm

DC=BC – BD = 25 - 10$\frac{5}{7}=14\frac{2}{7}$cm
${{S}_{\Delta ABD}}=\frac{1}{2}BD.AH$

${{S}_{\Delta ACD}}=\frac{1}{2}DC.AH$

$\Rightarrow \frac{{{S}_{\Delta ABD}}}{{{S}_{\Delta ACD}}}=\frac{DB}{DC}=\frac{3}{4}$