In triangle ABC, the bisector of angle BAC meets BC at point D in such a way that AB = 10 cm. AC = 15 cm and BD = 6 cm. Find the length of BC (in cm).

15

In triangle ABC,

 AB = 10 cm,

AC = 15 cm and BD = 6 cm.

We know,

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

According to the question,

If bisector of ∠ A is Δ ABC meets BC in D

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

= \(\frac{DC}{BD}\) = \(\frac{15a}{10a}\)

= \(\frac{DC}{6}\) = \(\frac{15}{10}\)

= DC = 9 cm

BC = BD + DC = 6 + 9 = 15 cm