Quantitative Aptitude Ques 2442

Question: In a $ \Delta ABC, $ it is given that AD is the internal bisector of $ \angle A. $ If $ AB=10,cm, $ $ AC=14cm $ and $ BC=6cm. $ Then, CD is equal to

Options:

A) 4.8 cm

B) 3.5 cm

C) 7 cm

D) 10.5 cm

Show Answer

Answer:

Correct Answer: B

Solution:

  • Let CD be x cm. Then, $ BD=(6-x),cm $ Now, BD: CD = AB: AC

$ \Rightarrow $ $ \frac{6-x}{x}=\frac{10}{14}=\frac{5}{7} $

$ \Rightarrow $ $ 42-7x=5x $

$ \Rightarrow $ $ 12x=42 $
$ \Rightarrow $ $ x=3.5 $

$ \therefore $ $ CD=3.5,cm $

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