Question

In the figure, PQRS is a parallelogram with and QR = 10 cm. L is a point on PR. RL : LP = 2 : 3. QL produced meets RS and PS produced at M. Select the statements that are true.

• A. $PN=50\text{cm}$
• B. $RM=20\frac{2}{3}\text{cm}$.
• C. $RM=10\frac{2}{3}\text{cm}$.
• D. $PN=15\text{cm}$

Answer 1

Answer: (C), (D)

The correct options are
C

$RM=10\frac{2}{3}\text{cm}$.

D

$PN=15\text{cm}$

In $\Delta LMP$ and $\Delta RLQ$

$\angle LMP=\angle LQR$ (Alternate angles)

(Vertically opposite angles)

(AA Postulate)

$\Rightarrow \frac{PM}{10}=\frac{3}{2}$ ($\because$ LP : RL = 3 : 2)

$\therefore PM=\frac{10\times 3}{2}=15\text{cm}$

Similarly, we can prove that

$\Delta LMR$ and $\Delta LPQ$ are similar.

$\therefore \frac{RM}{QP}=\frac{RL}{LP}$

$\therefore \frac{RM}{16}=\frac{2}{3}\Rightarrow RM=\frac{16\times 2}{3}=\frac{32}{3}\text{cm}$

$\therefore RM=10\frac{2}{3}\text{cm}$.