Given a triangle ABC, consider the bisector of ∡A which intersects BC at the point D.
If CD+AC=12 cm and CD=BC/3, What is the perimeter of the triangle (in cm)?
BC = 3CD => BD + CD = 3CD => BD = 2CD
AC/CD = AB/BD => AC/CD = AB/2CD => AB = 2AC
Perimeter = AC + BC + AB = AC + 3CD + 2AC = AC + CD + 2(AC + CD) = 3(AC + CD) = 3(12) = 36 cm.
