In the given figure, if QR XY = 149 and PY = 18 cm, then what is the value (in cm) of PQ?

In the given figure, if $$\frac{\text{QR}}{\text{XY}}=\frac{14}{9}$$   and PY = 18 cm, then what is the value (in cm) of PQ?

Answer: Option A

Solution

Answer: Option A

Solution:

$$\begin{array}{rl}& \angle QXY=120^{\circ }\\ & \angle PXY=60^{\circ }\\ & \Delta PXY\sim \Delta PRQ\\ & \therefore \frac{PY}{PQ}=\frac{XY}{QR}\\ & \frac{18}{PQ}=\frac{9}{14}\\ & PQ=\frac{18\times 14}{9}=28\text{cm}\end{array}$$