question_answer

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

A) \[4.8\,\,cm\]                  

B) \[3.5\,\,cm\]

C) \[7\,\,cm\]                     

D) \[10.5\,\,cm\]

Correct Answer: B

Solution :

Let CD be \[x\,\,cm.\]

Then,  \[BD=(6-x)\,\,cm\]

Now,     \[\frac{BD}{CD}=\frac{AB}{AC}\]

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

\[\Rightarrow \]   \[42-7x=5x\]\[\Rightarrow \]\[12x=42\]

\[\therefore \]      \[x=3.5\]