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).
Answer & explanation
Correct answer: option 3
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