| In a \[\Delta ABC,\]it is given that AD is the internal bisector of \[\angle A.\] If \[AB=10\,cm,\] \[AC=14\text{ }cm\]and \[BC=6\text{ }cm.\] 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, 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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