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).
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 15
Given:
In triangle ABC, the bisector of angle BAC meets BC at point D
AB = 10 cm, AC = 15 cm and BD = 6 cm
Concept used:
Angle bisector theorem states that an angle bisector of an angle of a triangle divides the opposite side into two parts that are proportional to the other two sides of the triangle.
Calculations:
Now, according to the question;
⇒ DC/BD = AC/AB
⇒ DC/6 = 15/10
⇒ DC = 9 cm
BC = BD + DC
BC = 9 + 6 = 15 cm