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(D) Given that $\Delta ABC \sim \Delta XYZ$ under the correspondence $ABC \leftrightarrow ZYX$. This implies that the ratios of corresponding sides ar

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$16$

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(D) Given that $\Delta ABC \sim \Delta XYZ$ under the correspondence $ABC \leftrightarrow ZYX$. This implies that the ratios of corresponding sides are equal: $\frac{AB}{ZY} = \frac{BC}{YX} = \frac{CA}{XZ} = k$. From the given values,$AB = 3, BC = 5, CA = 6$ and $XY = 6$. Using the correspondence $ABC \leftrightarrow ZYX$,we have the ratios: $\frac{AB}{ZY} = \frac{BC}{YX} = \frac{CA}{XZ}$. Substituting the known values: $\frac{3}{ZY} = \frac{5}{6} = \frac{6}{XZ}$. From $\frac{5}{6} = \frac{3}{ZY}$,we get $ZY = \frac{3 	imes 6}{5} = \frac{18}{5} = 3.6$. From $\frac{5}{6} = \frac{6}{XZ}$,we get $XZ = \frac{6 	imes 6}{5} = \frac{36}{5} = 7.2$. The perimeter of $\Delta XYZ = XY + YZ + ZX = 6 + 3.6 + 7.2 = 16.8$.

$\Delta ABC \sim \Delta XYZ$ for the correspondence $ABC \leftrightarrow ZYX$. If $AB = 3, BC = 5, CA = 6$ and $XY = 6$,find the perimeter of $\Delta XYZ$. (in $.8$)

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