Question

In a ΔABC, the bisector of ∠A intersects BC at D. If BD: DC = 4 : 7 and AC = 3.5 then AB = 

(A) 2 

(B) 3 

(C) 4 

(D) 5

Answer 1

Correct option is (A) 2

AD is angle bisector of \(\angle A\) which meet BC at D.

\(\therefore\) \(\frac{BD}{DC}=\frac{AB}{AC}\)      (By internal angle bisector theorem)

\(\Rightarrow\) \(AB=AC.\frac{BD}{DC}\)

\(=3.5\times\frac47\)

\(=0.5\times4=2\)    \((\because \frac{BD}{DC}=\frac47\;\&\;AC=3.5\) (given))

Answer 2

Correct option is: (A) 2