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

Vedclass · Accepted Answer

$14$

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(D) Given that $\Delta ABC \sim \Delta XYZ$ under the correspondence $ABC \leftrightarrow XZY$.This implies that the ratio of the corresponding sides is equal to the ratio of their perimeters.Therefore,$\frac{AB}{XZ} = \frac{BC}{ZY} = \frac{AC}{XY} = \frac{	ext{Perimeter of } \Delta ABC}{	ext{Perimeter of } \Delta XYZ}$.Given: $	ext{Perimeter of } \Delta ABC = 45$,$	ext{Perimeter of } \Delta XYZ = 30$,and $AB = 21$.Substituting the values into the ratio: $\frac{21}{XZ} = \frac{45}{30}$.Simplifying the fraction $\frac{45}{30}$ gives $\frac{3}{2}$.So,$\frac{21}{XZ} = \frac{3}{2}$.Cross-multiplying gives $3 	imes XZ = 21 	imes 2$.$3 	imes XZ = 42$.$XZ = \frac{42}{3} = 14$.Thus,the length of $XZ$ is $14$.

If $\Delta ABC \sim \Delta XYZ$ under the correspondence $ABC \leftrightarrow XZY$,and the perimeter of $\Delta ABC$ is $45$,the perimeter of $\Delta XYZ$ is $30$,and $AB = 21$,find the length of $XZ$.

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