Question

in the figure given below 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.

◆pls give solution with proper steps.
◆20 points !

# ch- similarity , class 10 th .

Answer 1

.(i) In the triangle RLQ and triangle PLN
angle RLQ = angle PLN
angle LRQ = angle LPN
therefore triangle RLQ ~ triangle PLN   (AA)
RQ/PN=RL/LP=2x/3x
=10/PN = 2/3 = PN = 15cm
(ii) triangle RLM ~ triangle PLQ (AA)
RM  =  LM   = RL
PQ      QL       LP
RM  = 2x
16       3x

Answer 2

Hi friend,

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!