1.

In ΔABC, the bisector of ∠A intersects side BC at D. If AB = 12 cm, AC = 15 cm and BC = 18 cm, then the length of BD is1. 8 cm2. 9.6 cm3. 7.5 cm4. 9 cm

Answer» Correct Answer - Option 1 : 8 cm

Given:

AB = 12 cm

AC = 15 cm

BC = 18 cm

Concept used:

The angle bisector of an angle of a triangle divides the opposite side into two parts that are proportional to the other two sides of the triangle.

Calculations:

The length of BC is, 

BC = BD + DC

⇒ DC = 18 – BD

Using the concept,

⇒ BD/DC = AB/AC

⇒ BD/(18 – BD) = 12/15

⇒ BD/(18 – BD) = 4/5

⇒ 5BD = 72 – 4BD

⇒ 9BD = 72 

⇒ BD = 8 cm

∴ The length of BD is 8 cm



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