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(B) In $\Delta XYZ$,$XM$ is the bisector of $\angle X$,which intersects $\overline{YZ}$ at $M$.According to the Angle Bisector Theorem,the ratio of th

Vedclass · Accepted Answer

$9.8$

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(B) In $\Delta XYZ$,$XM$ is the bisector of $\angle X$,which intersects $\overline{YZ}$ at $M$.According to the Angle Bisector Theorem,the ratio of the sides forming the angle is equal to the ratio of the segments of the opposite side.$	herefore \frac{XY}{XZ} = \frac{YM}{MZ}$Substituting the given values:$	herefore \frac{6}{8} = \frac{4.2}{MZ}$$	herefore MZ = \frac{4.2 	imes 8}{6}$$	herefore MZ = 0.7 	imes 8 = 5.6$Now,$YZ = YM + MZ$ (since $Y-M-Z$ are collinear).$YZ = 4.2 + 5.6 = 9.8$.

In $\Delta XYZ$,the bisector of $\angle X$ intersects $\overline{YZ}$ at $M$. If $XY = 6$,$XZ = 8$ and $YM = 4.2$,find $YZ$.

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