A parallelogram PQRS has side length 5 and 10 cm. M is the mid point of PQ what is the area of the triangle MRS
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In the figure, PQRS is a parallelogram with PQ=15cm and RQ=10cm. L is a point on RP such that RL:LP=2:3. QL produced meets RS at M and PS produced at N. Find the lengths of PN and RM.
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Correct option is A)
Given: PQRS is a parallelogram. PQ=15 and RQ=10,
LP
RL
=
3
2
In △RLQ and △NLP
∠RLQ=∠NLP (vertically opposite angles)
∠LRQ=∠LPN (Alternate angles)
∠LQR=∠LNP (Alternate angles)
Thus, △RLQ∼△PLN (AAA rule)
Hence,
PL
RL
=
PN
RQ
(Corresponding sides of similar triangles)
PN=
2
3×10
PN=15cm
Similarly, △RLM∼△PLQ
LP
RL
=
PQ
RM
(Corresponding sides of similar triangles)
RM=
3
15×2
RM=10 cm.
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Answer:
Given: PQRS is a parallelogram. PQ=15 and RQ=10,
LP
RL
=
3
2
In △RLQ and △NLP
∠RLQ=∠NLP (vertically opposite angles)
∠LRQ=∠LPN (Alternate angles)
∠LQR=∠LNP (Alternate angles)
Thus, △RLQ∼△PLN (AAA rule)
Hence,
PL
RL
=
PN
RQ
(Corresponding sides of similar triangles)
PN=
2
3×10
PN=15cm
Similarly, △RLM∼△PLQ
LP
RL
=
PQ
RM
(Corresponding sides of similar triangles)
RM=
3
15×2
RM=10 cm.