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(D) Given the correspondence $ABC \leftrightarrow XZY$,the triangles are similar,i.e.,$\Delta ABC \sim \Delta XZY$.
From the property of similar tria

Vedclass · Accepted Answer

$18$

Vedclass · Answer

(D) Given the correspondence $ABC \leftrightarrow XZY$,the triangles are similar,i.e.,$\Delta ABC \sim \Delta XZY$.
From the property of similar triangles,the ratio of corresponding sides is equal:
$\frac{AB}{XZ} = \frac{BC}{ZY} = \frac{AC}{XY}$.
Given $AB = 6$,$XY = 12$,$YZ = 6$,and $ZX = 9$.
Using the correspondence $ABC \leftrightarrow XZY$,the sides are proportional as follows:
$\frac{AB}{XZ} = \frac{BC}{ZY} = \frac{AC}{XY}$
$\frac{6}{9} = \frac{BC}{6} = \frac{AC}{12}$
First,find $BC$: $\frac{6}{9} = \frac{BC}{6} \implies BC = \frac{6 	imes 6}{9} = \frac{36}{9} = 4$.
Next,find $AC$: $\frac{6}{9} = \frac{AC}{12} \implies AC = \frac{6 	imes 12}{9} = \frac{72}{9} = 8$.
The perimeter of $\Delta ABC = AB + BC + AC = 6 + 4 + 8 = 18$.

$\Delta ABC$ and $\Delta XYZ$ are similar under the correspondence $ABC \leftrightarrow XZY$. If $AB = 6$,$XY = 12$,$YZ = 6$,and $ZX = 9$,find the perimeter of $\Delta ABC$.

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