In a triangle ABC, AD is the bisector of \angle BAC. If AB=12 cm, BD=10 cm and DC=5 cm, then what is the perimeter of the triangle?

Explanation

Using the angle bisector theorem, \frac{AB}{AC} = \frac{BD}{DC}. We get \frac{12}{AC} = \frac{10}{5} = 2 \implies AC = 6 cm. The perimeter is the sum of all sides: AB + BC + AC = 12 + (10 + 5) + 6 = 33 cm.

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