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(C) Since $\Delta ABC \sim \Delta DEF$,the ratios of their corresponding sides are equal:$\frac{AB}{DE} = \frac{AC}{DF} = \frac{BC}{EF} = k$Given $AB

Vedclass · Accepted Answer

$45$

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(C) Since $\Delta ABC \sim \Delta DEF$,the ratios of their corresponding sides are equal:$\frac{AB}{DE} = \frac{AC}{DF} = \frac{BC}{EF} = k$Given $AB = 8$,$DE = 12$,$AC = 10$,and $EF = 18$.The ratio of similarity $k = \frac{AB}{DE} = \frac{8}{12} = \frac{2}{3}$.Now,find the remaining sides of $\Delta DEF$:$\frac{AC}{DF} = \frac{2}{3} \implies \frac{10}{DF} = \frac{2}{3} \implies DF = \frac{10 	imes 3}{2} = 15$.$\frac{BC}{EF} = \frac{2}{3} \implies \frac{BC}{18} = \frac{2}{3} \implies BC = \frac{18 	imes 2}{3} = 12$.Now,find the perimeter of $\Delta DEF = DE + EF + DF = 12 + 18 + 15 = 45$.

If $\Delta ABC \sim \Delta DEF$ for the correspondence $ABC \leftrightarrow DEF$,and given $AB = 8$,$AC = 10$,$DE = 12$,and $EF = 18$,find the perimeter of $\Delta DEF$.

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