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PQRS is a parallclogram such that PQ is ...

PQRS is a parallclogram such that PQ is parallel to SR and SP is parallel to RQ. The length of side PQ is 20 cm. M is point between P and Q such that the length of PM is 3 cm. N is a points between points S and R. Find the length of SN such that segmen MN divides the paralelogram in two regions with equal areas.

Text Solution

Verified by Experts

Let h be the perpendicular distance between PQ and SR.
Since PQ = 20 cm and PM = 3 cm
`thereforeMQ=20-3=17cm`
Also, `SR=PQ=20cm" "("becauseopposite sides of a parallelogram are equal")`
Now, `ar(Trap.PMNS)=ar(Trip.MQRN)(given)`
`implies" "1/2xxh(PM+SN)=1/2xxh(MQ+NR)`
`implies" "3+SN=17+(SR-SN)`
`implies" "2.SN=17+20-3=34`
`=" "SN =17cm.`
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