Question : In $\triangle$PQR, a straight line parallel to the base, QR cuts PQ at X and PR at Y. If PX : XQ = 5 : 6, then XY : QR will be:
Option 1: 5 : 11
Option 2: 6 : 5
Option 3: 11 : 6
Option 4: 11 : 5
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Correct Answer: 5 : 11
Solution :
Given:
In $\triangle$PQR, QR || XY
$\frac{PX}{XQ}=\frac{5}{6}$
Let PX = 5 units, XQ = 6 units
So, PQ = 5 + 6 = 11 units
In ∆ PXY and ∆ PQR,
∵ QR | | XY
∵ $\angle$X = $\angle$Q ; $\angle$Y = $\angle$R
∴ By AA - similarity,
Here, $\triangle$PXY $\simeq \triangle$PQR
$\frac{PX}{PQ}=\frac{XY}{QR}$
⇒ $\frac{5}{11}=\frac{XY}{QR}$
$\therefore XY: QR=5:11$
Hence, the correct answer is 5 : 11.
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