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?

Solution (By Examveda Team)

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