Delta PQR sim Delta XYZ for the correspondenc | vedclass

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(C) Given that $\Delta PQR \sim \Delta XYZ$ for the correspondence $PQR \leftrightarrow XZY$.According to the theorem of areas of similar triangles,th

Vedclass · Accepted Answer

$54$

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(C) Given that $\Delta PQR \sim \Delta XYZ$ for the correspondence $PQR \leftrightarrow XZY$.According to the theorem of areas of similar triangles,the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.Therefore,$\frac{	ext{Area of } \Delta PQR}{	ext{Area of } \Delta XYZ} = \frac{PQ^2}{XZ^2}$.Substituting the given values: $\frac{24}{	ext{Area of } \Delta XYZ} = \frac{8^2}{12^2}$.$\frac{24}{	ext{Area of } \Delta XYZ} = \frac{64}{144}$.Simplifying the fraction: $\frac{64}{144} = \frac{4}{9}$.So,$\frac{24}{	ext{Area of } \Delta XYZ} = \frac{4}{9}$.$	ext{Area of } \Delta XYZ = \frac{24 	imes 9}{4} = 6 	imes 9 = 54$.

$\Delta PQR \sim \Delta XYZ$ for the correspondence $PQR \leftrightarrow XZY$. If $PQ = 8$,$XZ = 12$ and the area of $\Delta PQR$ is $24$,find the area of $\Delta XYZ$.

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