In triangle ABC, AD is the bisector of angle BAC. If AB=10 cm, AC=14 cm and BC=6 cm, find BD and DC.
Pls solve it without angle bisector property..pls...

Dear Student,


In $∆$ ABC we have AD as bisector of $\angle$BAC
Therefore,
$\frac{\mathrm{AB}}{\mathrm{AC}}=\frac{\mathrm{BD}}{\mathrm{CD}}$
Now, AB = 10cm , AC = 14cm , BC = 6cm
​Let BD = x cm, then CD = (6 - x) cm

Now, $\frac{\mathrm{AB}}{\mathrm{AC}}=\frac{\mathrm{BD}}{\mathrm{CD}}$
$\frac{10}{14}=\frac{\mathrm{x}}{6-\mathrm{x}}$

$\frac{5}{7}=\frac{\mathrm{x}}{6-\mathrm{x}}$
5 (6-x) = 7x
30 - 5x = 7x
12x = 30
x = 2.5 cm

Hence, BD = 2.5 cm and CD = 6 - 2.5 = 3.5 cm

Regards