M is the mid-point of side QR of a parallelogram PQRS (P being on the top left hand, followed by other points going clockwise). The line SM is drawn intersecting PQ produced at T. What is the length (in terms of the length of SR) of PT?

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SSC CHSL Exam 2023 Tier-I Official Paper (Held On: 10 Aug, 2023 Shift 1)
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  1. \(\frac{3 \mathrm{SR}}{2}\)
  2. \(\frac{\mathrm{SR}}{2}\)
  3. 2SR
  4. SR

Answer (Detailed Solution Below)

Option 3 : 2SR
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Detailed Solution

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Given:

M is the mid-point of side QR of a parallelogram PQRS

The line SM is drawn intersecting PQ produced at T.

Calculation:

F1 Vinanti SSC 05.12.23 D13

QM parallel to PS , and QM = MR

So we can say that PQ = QT

Again, PQ = SR

Now PT = 2PQ

So  PT = 2SR [ opposite sides of parallelogram]

∴ The correct option is 3

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