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

Correct option is C

Given:

PQRS is a parallelogram.

M is the midpoint of QR.

SM is drawn and intersects PQ (produced) at T.

Theorem Used:

In a parallelogram, if a line from a vertex to the midpoint of the opposite side is extended to meet the extended side of the parallelogram, it divides the extended side in the ratio 2:1.      

 

QM parallel to be PS, and QM = QT 

So we can say that PQ = QT 

Again PQ = SR

Now PT = 2PQ 

So PT= 2SR (Opposite sides of  parallelogram.