The bisector of ∠ B in △ABC meets AC at D. If AB = 12 cm. BC = 18 cm and AC = 15 cm then the length of AD (in cm) is :

6

Here, the bisector of \(\angle\)B in \(\Delta \)ABC meets AC at D

So, \(\frac{BC}{AB}\) = \(\frac{CD}{AD}\)

⇒ \(\frac{18}{12}\) = \(\frac{CD}{AD}\)

⇒ \(\frac{CD}{AD}\) = \(\frac{3}{2}\)

Let CD and AD be 3x and 2x respectively,

Given, AC = 15 cm

AD + CD = 15

⇒ 2x + 3x = 15

⇒ x = 3,

So, AD = 2x = 6 cm

Therefore, the length of AD is 6 cm.