The bisector of $\angle \mathrm{A}$ in $\triangle \mathrm{ABC}$ meets side $\mathrm{BC}$ at $\mathrm{D}$. If $\mathrm{AB}=12 \mathrm{~cm}, \mathrm{AC}=15 \mathrm{~cm}$ and $\mathrm{BC}=18 \mathrm{~cm}$, then the length of $\mathrm{DC}$ is:

10 cm

The length of BC is,

BC = BD + DC

= BD = 18 - DC

Using the concept,

= \(\frac{BD}{DC}\) = \(\frac{AB}{AC}\)

= \(\frac{18\;-\;DC}{DC}\) = \(\frac{12}{15}\)

= \(\frac{18\;-\;DC}{DC}\) = \(\frac{4}{5}\)

= 90 - 5DC = 4DC

= 9DC = 90

= DC = 10 cm

Therefore, DC is 10 cm.