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(D) 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

$12$

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(D) 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 $\Delta XYZ,$ since $XT$ is the bisector of $\angle X,$ we have the ratio: $\frac{XY}{XZ} = \frac{YT}{TZ}$.Given $XY = 10, XZ = 14,$ and $YT = 5.$Substituting these values into the equation: $\frac{10}{14} = \frac{5}{TZ}$.Simplifying the ratio: $\frac{5}{7} = \frac{5}{TZ}$.Therefore,$TZ = 7.$The total length of $YZ$ is the sum of $YT$ and $TZ$: $YZ = YT + TZ = 5 + 7 = 12.$

In $\Delta XYZ,$ the bisector of $\angle X$ intersects $\overline{YZ}$ at $T$. If $XY = 10, XZ = 14$ and $YT = 5,$ find $YZ.$

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