Delta ABC sim Delta PQR for the correspondenc | vedclass

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(A) Given that $\Delta ABC \sim \Delta PQR.$ According to the properties of similar triangles,the ratio of their perimeters is equal to the ratio of t

Vedclass · Accepted Answer

$9$

Vedclass · Answer

(A) Given that $\Delta ABC \sim \Delta PQR.$ According to the properties of similar triangles,the ratio of their perimeters is equal to the ratio of their corresponding sides. Therefore,$\frac{	ext{Perimeter of } \Delta ABC}{	ext{Perimeter of } \Delta PQR} = \frac{AB}{PQ}.$ Substituting the given values: $\frac{16}{24} = \frac{6}{PQ}.$ Simplifying the ratio $\frac{16}{24}$ gives $\frac{2}{3}.$ So,$\frac{2}{3} = \frac{6}{PQ}.$ Cross-multiplying gives $2 	imes PQ = 18.$ Thus,$PQ = \frac{18}{2} = 9.$ The correct option is $A$.

$\Delta ABC \sim \Delta PQR$ for the correspondence $ABC \leftrightarrow PQR.$ The perimeter of $\Delta ABC$ is $16$ and the perimeter of $\Delta PQR$ is $24.$ If $AB = 6$,find $PQ$.

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