Delta PQR sim Delta XYZ for the correspondenc | vedclass

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(B) Given that $\Delta PQR \sim \Delta XYZ$ for the correspondence $PQR \leftrightarrow XYZ$.Since the triangles are similar,the ratios of their corre

Vedclass · Accepted Answer

$7.5$

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(B) Given that $\Delta PQR \sim \Delta XYZ$ for the correspondence $PQR \leftrightarrow XYZ$.Since the triangles are similar,the ratios of their corresponding sides are equal.Given $PQ : QR : PR = 3 : 5 : 7$,it follows that $XY : YZ : XZ = 3 : 5 : 7$.Let $XY = 3t$,$YZ = 5t$,and $XZ = 7t$ for some constant $t > 0$.The perimeter of $\Delta XYZ$ is given as $22.5$.Therefore,$XY + YZ + XZ = 22.5$.Substituting the values in terms of $t$: $3t + 5t + 7t = 22.5$.$15t = 22.5$.$t = \frac{22.5}{15} = 1.5$.Now,calculating $YZ$: $YZ = 5t = 5 	imes 1.5 = 7.5$.

$\Delta PQR \sim \Delta XYZ$ for the correspondence $PQR \leftrightarrow XYZ$. If $PQ : QR : PR = 3 : 5 : 7$ and the perimeter of $\Delta XYZ$ is $22.5$,then $YZ = \ldots$

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