Delta PQR sim Delta XYZ for the correspondenc | vedclass

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(A) Given that $\Delta PQR \sim \Delta XYZ$.For similar triangles,the ratio of their perimeters is equal to the ratio of their corresponding sides.The

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$25$

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(A) Given that $\Delta PQR \sim \Delta XYZ$.For similar triangles,the ratio of their perimeters is equal to the ratio of their corresponding sides.Therefore,$\frac{	ext{Perimeter of } \Delta PQR}{	ext{Perimeter of } \Delta XYZ} = \frac{PR}{XZ}$.Given values are: Perimeter of $\Delta PQR = 24$,Perimeter of $\Delta XYZ = 60$,and $PR = 10$.Substituting these values into the formula: $\frac{24}{60} = \frac{10}{XZ}$.Simplifying the fraction $\frac{24}{60}$ gives $\frac{2}{5}$.So,$\frac{2}{5} = \frac{10}{XZ}$.Cross-multiplying gives $2 	imes XZ = 50$.$XZ = \frac{50}{2} = 25$.Thus,$XZ = 25$.

$\Delta PQR \sim \Delta XYZ$ for the correspondence $PQR \leftrightarrow XYZ$. The perimeter of $\Delta PQR$ is $24$ and the perimeter of $\Delta XYZ$ is $60$. If $PR = 10$,find $XZ$.

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