In Delta XYZ,the bisector of angle X intersec | vedclass

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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

$11.2$

Vedclass · Answer

(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 $\Delta XYZ$,$XM$ is the bisector of $\angle X$,so $\frac{XY}{XZ} = \frac{YM}{MZ}$.Given $XY = 8$,$XZ = 6$,and $MZ = 4.8$.Substituting the values: $\frac{8}{6} = \frac{YM}{4.8}$.Simplify the fraction: $\frac{4}{3} = \frac{YM}{4.8}$.Solving for $YM$: $YM = \frac{4 	imes 4.8}{3} = 4 	imes 1.6 = 6.4$.The length of $YZ = YM + MZ$.$YZ = 6.4 + 4.8 = 11.2$.

In $\Delta XYZ$,the bisector of $\angle X$ intersects $\overline{YZ}$ at $M$. If $XY = 8$,$XZ = 6$ and $MZ = 4.8$,find $YZ$.

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