Question

In $△$ ABC, the bisector of $\angle$ A intersects BC in D. If AB = 18 cm, AC = 15 cm and BC = 22 cm, find BD.

Answer 1

Given $AB=18$ cm, $AC=15$ cm and $BC=22$ cm

By angle bisector theorem, if bisector of $\angle A$ meets side $BC$ at $D$, then

$\frac{AB}{AC}=\frac{BD}{DC}$

$\frac{AB}{AC}=\frac{BD}{BC-BD}$

Substituting values of $AB,AC$ and $BC$

$\frac{18}{15}=\frac{BD}{22-BD}$

$\frac{6}{5}=\frac{BD}{22-BD}$

$(22\ast 6)-6BD=5BD$

$\therefore BD=12$cm.