In Delta PQR,P-X-Q,P-Y-R and overline{XY} par | vedclass

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(C) Given that $\overline{XY} \parallel \overline{QR}$ in $\Delta PQR$. By the Basic Proportionality Theorem (Thales Theorem) and the property of simi

Vedclass · Accepted Answer

$30.25$

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(C) Given that $\overline{XY} \parallel \overline{QR}$ in $\Delta PQR$. By the Basic Proportionality Theorem (Thales Theorem) and the property of similar triangles,$\Delta PXY \sim \Delta PQR$. Since the triangles are similar,the ratio of their corresponding sides is equal: $\frac{XY}{QR} = \frac{PY}{PR}$. We are given $PY = 4$ and $YR = 7$. Therefore,$PR = PY + YR = 4 + 7 = 11$. Substituting the values into the ratio: $\frac{11}{QR} = \frac{4}{11}$. Cross-multiplying to solve for $QR$: $4 	imes QR = 11 	imes 11$. $4 	imes QR = 121$. $QR = \frac{121}{4} = 30.25$.

In $\Delta PQR$,$P-X-Q$,$P-Y-R$ and $\overline{XY} \parallel \overline{QR}$. If $PY = 4$,$YR = 7$ and $XY = 11$,find $QR$.

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