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

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(A) 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

$6$

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(A) 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: $\frac{BD}{DC} = \frac{AB}{AC}$.Given that $AB : AC = 3 : 4$,it follows that $\frac{BD}{DC} = \frac{3}{4}$.Let $BD = 3x$ and $DC = 4x$.We are given that $BC = 14$,so $BD + DC = 14$.Substituting the values,we get $3x + 4x = 14$,which simplifies to $7x = 14$.Solving for $x$,we find $x = 2$.Therefore,$BD = 3x = 3(2) = 6$.

In $\Delta ABC$,the bisector of $\angle A$ intersects $\overline{BC}$ at $D$. If $AB : AC = 3 : 4$ and $BC = 14$,find $BD$.

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