In the figure given below, PQRS is a parallelogram; PQ=16cm,QR=10cm.L is a point on PR such that RL:LP=2:3:QL produced meets RS at M and PS produced at N. Prove that triangle RLQ is similar to triangle PLN. Hence, find PN.
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Solution
From the question it is give that, Consider the △RLQ and △PLN, ∠RLQ=∠NLP [vertically opposite angles are equal] ∠RQL=∠LNP [alternate angle are equal] Therefore, △RLQ∼△PLN So, QR/PN=RL/LP=2/3 QR/PN=2/3 10/PN=2/3 PN=(10×3)/2 PN=30/2 PN=15cm Therefore, PN=15cm.