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Mathematics

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.

Mid-point Theorem

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Answer

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

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Assertion (A): Using the information in the given figure, we get CE : EA = 5:3.
Reason (R): Since, ∠ADE = ∠ABC = 90°
so, $\dfrac{CE}{EA} = \dfrac{BD}{AD} = \dfrac{8-5}{5} = \dfrac{3}{5}$
⇒ CE : EA = 3 : 5
A is true, R is false.
A is false, R is true.
Both A and R are true.
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