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).
Answer & explanation
Correct answer: option 4
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.