In Delta ABC, the bisector of angle A interse | vedclass

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(C) According to the Angle Bisector Theorem,the bisector of an angle of a triangle divides the opposite side into segments that are proportional to th

Vedclass · Accepted Answer

$2.8$

Vedclass · Answer

(C) According to the Angle Bisector Theorem,the bisector of an angle of a triangle divides the opposite side into segments that are proportional to the other two sides of the triangle.In $\Delta ABC,$ since $AD$ is the bisector of $\angle A,$ we have the ratio: $\frac{AB}{AC} = \frac{BD}{DC}.$Given $BC = 5$ and $DC = 3,$ we can find $BD$ as: $BD = BC - DC = 5 - 3 = 2.$Now,substitute the known values into the ratio: $\frac{AB}{4.2} = \frac{2}{3}.$Solving for $AB$: $AB = \frac{2 	imes 4.2}{3} = \frac{8.4}{3} = 2.8.$Therefore,the length of $AB$ is $2.8.$

In $\Delta ABC,$ the bisector of $\angle A$ intersects $\overline{BC}$ at $D.$ If $AC = 4.2,$ $DC = 3,$ and $BC = 5,$ find $AB.$

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