Question

PQRS is a parallelogram; PQ = 16 cm, 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. (i) Prove that triangle RLQ is similar to triangle PLN. Hence find PN. (ii) Name a triangle similar to triangle RLM. Evaluate RM.

Answer 1

Answer:Hi friend,

Step-by-step explanation:Your answer with proper steps :-

In the given figure,

In triangle RLQ and triangle PLN,

∠ RLQ = ∠ PLN

∠ LRQ = ∠ LPN

Hence, it is proved that triangle RLQ ~ triangle PLN   (by AA criterion)

=> QR / PN = RL / LP

                 

                   = 2x/3x

=>10/PN = 2/3                      (QR = 10)

=> PN = 15cm

Now,

(ii) Let RL = 2x and LP = 3x

As triangle RLM ~ triangle PLQ (proved by AA criterion)

=> RM/PQ  =  LM/QL   = RL/LP

=> RM/16  = 2x / 3x

=> RM = (2 x 16) / 3  cm.

=> RM = 32 / 3 cm

Hope it helps!