Question

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$<b>In ∆ABC, the bisector of angle A intersects BC at D if AB equal to 18 cm, AC equal to 15 cm and BC = 22 cm ,find BD</b>$

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Answer 1

$\mathsf{\huge{Question}}$

In △ABC, the bisector of ∠A intersects at BC at D. If AB = 18 cm, AC = 15 cm and BC = 22cm, find BD.

$\mathsf{\huge{Answer}}$

BD = 12 cm

$\mathsf{\huge{Explaination}}$

$\bold{Given\:that,}$

AB = 18 cm

AC = 15 cm

BC = 22 cm

$\bold{To\:find,}$

BD = ?

Let BD be represented as x.

In the above figure,

DC = 22-x

As, it is given that,

BC = 22 cm.

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

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

18(22-x) = 15x

396 - 18x = 15x

396 = 18x + 15x

396 = 33x

x = $\frac{396}{33}$

x = 12cm.