In a triangle ABC, the bisector of angle BAC meets BC at point D such that DC = 2 BD. If AC - AB = 5 cm, then find the length of AB (in cm).

5

AD is the bisector of \(\angle\)BAC

⇒ \(\frac{AB}{AC}\) = \(\frac{BD}{DC}\)

Substituting the values, we get,

⇒ \(\frac{AB}{AB\; + \; 5}\) = \(\frac{BD}{2BD}\)

⇒ \(\frac{AB}{AB\; + \; 5}\) = \(\frac{1}{2}\)

⇒ 2AB = AB + 5

⇒ AB = 5 cm,

Therefore, the length of AB is 5 cm.