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 :
Answer & explanation
Correct answer: option 1
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.