Question
In $\triangle\text{ABC},$ the bisector of $\angle\text{A}$ intersects BC in D. If AB = 18cm, AC = 15cm and BC = 22cm, find BD.
✓
Answer
We have to find the value of BD.Given: AB = 18cm, AC = 15cm and BC = 22cm.
In $\triangle\text{ABC},$ AD the bisector of $\angle\text{A}.$
$\frac{\text{AB}}{\text{AC}}=\frac{\text{BD}}{\text{DC}}$
$\frac{\text{AB}}{\text{AC}}=\frac{\text{BD}}{\text{BC}-\text{BD}}$
$\frac{18}{15}=\frac{\text{BD}}{22-\text{BD}}$
On cross multiplication, we get,
6(22 - BD) = 5 × BD
132 - 6BD = 5BD
132 = 5BD + 6BD
132 = 11BD
$\text{BD}=\frac{132}{11}$
BD = 12cm
Hence, the value of BD is 12cm.
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