Question

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 $N$.
Name a triangle similar to triangle $RLM$. Evaluate $RM$.

Answer 1

From the figure,
Consider $△RLM$ and $△QLP$
Then, $\angle RLM=\angle QLP$ [vertically opposite angles are equal]
$\angle LRM=\angle LPQ$ [alternate angles are equal]
Therefore, $△RLM\sim △QLP$
Then, $RM/PQ=RL/LP=2/3$
So, $RM/16=2/3$
$RM=(16\times 2)/3$
$RM=32/3$
$RM=10\frac{2}{3}$.