In $Δ A B C$ , $A D$ is the bisector of $∠ B A C$ . If $A B = 10 c m, A C = 14 c m$ and $B C = 6 c m$ , then $B D$ is:

2.5 c m

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3 c m

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3.5 c m

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None of the above

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Solution

The correct option is A $2.5 c m$
In $△ A B C$ we have $A D$ as bisector of $∠ B A C$
$A B = 10 c m, A C = 14 c m, B C = 6 c m$
Let, $B D = x c m$ , then $C D = (6 - x) c m$

$∴ \frac{A D}{A C} = \frac{B D}{C D}$

$\frac{10}{14} = \frac{x}{6 - x}$

$\frac{5}{7} = \frac{x}{6 - x}$

$5 (6 - x) = 7 x$

$30 - 5 x = 7 x$

$12 x = 30$

$x = 2.5$

$∴ B D = 2.5 c m$ .

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Similar questions

In a $Δ A B C$ , AD is the bisector of $∠ A$ , meeting side BC at D.
(i) If BD= 2.5 cm, AB = 5 cm and AC = 4.2 cm, find DC.
(ii) If BD= 2 cm, AB = 5 cm and DC = 3 cm, find AC.
(iii) If AB= 3.5 cm, AC = 4.2 cm and DC = 2.8 cm, find BD.
(iv) If AB =10 cm, AC =14 cm and BC = 6 cm, find BD and DC.
(v) If AC = 4.2 cm, DC = 6 cm and BC = 10 cm, find AB.
(vi) If AD= 5.6 cm, AC = 6 cm and DC = 3 cm, find BC.
(vii) If AB= 3.6 cm, BC e 6 cm and BD = 32 cm, find AC.
(viii) If AB =10 cm, AC = 6 cm and BC = 12 cm, find BD and DC