In a - AD is the bisector of - ABC- meeting side BC at D- If AB - 10 cm- AC - 6 cm- BC - 12 cm- find BD-

The correct option is C 7.5 In Δ BAD and Δ #10;DAC, ∠ BAD = ∠ DAC ∠ ABD = #10;∠ ACD #10; #10; [since AD is commo ...

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Standard IX

Mathematics

Square

In a , AD i...

Question

In a , AD is the bisector of $Δ A B C$ , meeting side BC at D. If AB = 10 cm, AC = 6 cm, BC = 12 cm, find BD.

3.3

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18

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7.5

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1.33

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Solution

The correct option is C $7.5$
In $Δ B A D a n d Δ D A C, ∠ B A D = ∠ D A C ∠ A B D = ∠ A C D$

$[s i n c e A D i s c o m m o n, a n g l e s o p p o s i t e e q u a l s i d e s a r e e q u a l]$ .

Hence the triangles are similar by AA.

So, $\frac{A C}{A B} = \frac{D C}{D B} ⟹ \frac{6}{10} = \frac{12 - x}{x} ⟹ 6 x = 120 - 10 x ⟹ 16 x = 120 o r x = 7.5$ .

Hence BD = 7.5cm.

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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