In parallelogram PQRS, L is mid-point of side SR and SN is drawn parallel to LQ which meets RQ produced at N and cuts side PQ at M. Given, RN = 25 cm calculate the length of SP.

12.5 cm

Reason

In △ SRN :

L is mid-point of SR and LQ // SN [Given]

∴ LQ bisects RN [Line through mid-point of one side of a △ and parallel to another side bisects the third side]

i.e., RQ = QN = $\dfrac{1}{2}$ RN

⇒ RQ = $\dfrac{1}{2}$ RN

We know that,

Opposite sides of a parallelogram are equal.

∴ SP = $\dfrac{1}{2}RN = \dfrac{1}{2} \times 25$ = 12.5 cm