In Delta ABC and Delta XYZ,frac{AB}{XY} = fra | vedclass

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(A) Given that in $\Delta ABC$ and $\Delta XYZ$,$\frac{AB}{XY} = \frac{BC}{YZ}$ and $\angle B \cong \angle Y$.By the $SAS$ (Side-Angle-Side) similarit

Vedclass · Accepted Answer

$37.5$

Vedclass · Answer

(A) Given that in $\Delta ABC$ and $\Delta XYZ$,$\frac{AB}{XY} = \frac{BC}{YZ}$ and $\angle B \cong \angle Y$.By the $SAS$ (Side-Angle-Side) similarity criterion,$\Delta ABC \sim \Delta XYZ$.Since the triangles are similar,the ratios of their corresponding sides are equal:$\frac{AB}{XY} = \frac{AC}{XZ} = \frac{BC}{YZ}$.Substituting the given values:$\frac{6}{15} = \frac{15}{XZ}$.Cross-multiplying to solve for $XZ$:$6 	imes XZ = 15 	imes 15$.$6 	imes XZ = 225$.$XZ = \frac{225}{6} = 37.5$.Therefore,$XZ = 37.5$.

In $\Delta ABC$ and $\Delta XYZ$,$\frac{AB}{XY} = \frac{BC}{YZ}$ and $\angle B \cong \angle Y$. If $AB = 6$,$AC = 15$,and $XY = 15$,find $XZ$.

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