Question

--- In triangle ABC, the bisector of angle A intersects BC in D. Find BC if AB = 6 cm, AC = 5 cm and BD = 3 cm. find the value of BC = (?)​

Answer 1

Answer:

Let the given ∆ABC be as drawn below:

Here, we can see that ∠BAC is bisected by AD where AD touches BC at D. BC=BD+DC where, BC=3cm . We also have the values of adjacent sides AB=6cm and AC=5cm .

These satisfy the requirements of angle bisector theorem. Then, by the theorem, we have:

ABBD=ACDC

⇒DC=AC∗BDAB=5∗36=2.5cm

Happy math!!