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:
Answer & explanation
Correct answer: option 4
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.