Given: AD is the bisector of ∠BAC AB=12cm,BD=10cm,DC=5cm Concept used: Angle bisector theorem: The angle bisector of a triangle bisects the opposite side in such a way that the ratio of the two-line segments is proportional to the ratio of the other two sides. Perimeter = Sum of the three sides Calculation:
According to the concept, In △ABC , AB∕AC=BD∕DC ⇒12∕AC=10∕5 ⇒60=10AC ⇒60∕10=AC ⇒AC=6cm Now, Perimeter of △ABC=AB+BC+AC ⇒ Perimeter of ∆ABC=12+15+6[∵BC=BD+DC] ⇒ Perimeter of △ABC=33 ∴ The perimeter of the triangle is 33cm