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(B) 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

$11.4$

Vedclass · Answer

(B) 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.Therefore,$\frac{AB}{AC} = \frac{BD}{DC}$.Given $AB = 5.2$,$AC = 10.4$,and $BD = 3.8$.Substituting the values: $\frac{5.2}{10.4} = \frac{3.8}{DC}$.Since $\frac{5.2}{10.4} = \frac{1}{2}$,we have $\frac{1}{2} = \frac{3.8}{DC}$.Thus,$DC = 3.8 	imes 2 = 7.6$.Since $BC = BD + DC$,we have $BC = 3.8 + 7.6 = 11.4$.

In $\Delta ABC$,the bisector of $\angle A$ intersects $\overline{BC}$ at $D$. If $AB = 5.2$,$AC = 10.4$,and $BD = 3.8$,find $BC$.

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