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Question
In the figure, PQRS is a parallelogram with PQ = 16 cm and QR = 10 cm. L is a point on PR such that RL : LP = 2 : 3. QL produced meets RS at M and PS produced at N.
Find the lengths of PN and RM.
Solution
In ∆RLQ and ∆PLN,
∠RLQ = ∠PLN ...(Vertically opposite angles)
∠LRQ = ∠LPN ...(Alternate angles)
∆RLQ ~ ∆PLN ...(AA Similarity)
∴ `(RL)/(LP) = (RQ)/(PN)`
`2/3 = (10)/(PN)`
PN = 15 cm
In ∆RLM and ∆PLQ
∠RLM = ∠PLQ ...(Vertically opposite angles)
∠LRM= ∠LPQ ...(Alternate angles)
∆RLM ~ ∆PLQ ...(AA Similarity)
∴ `(RM)/(PQ) = (RL)/(LP)`
`(RM)/16 = 2/3`
`RM = 32/3 = 10 2/3 cm`
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