In the given figure, AQ = 4√2 cm, QC = 6√2 cm and AB = 20 cm. If PQ is parallel to BC, then what is the value (in cm) of PB?

$$\eqalign{ & {\text{In }}\Delta APQ\,\& \,\Delta ABC \cr & \frac{{AP}}{{AB}} = \frac{{AQ}}{{AC}} \cr & \frac{{AP}}{{20}} = \frac{{4\sqrt 2 }}{{10\sqrt 2 }} \cr & AP = \frac{{20 \times 2}}{5} = 8{\text{ cm}} \cr & PB = AB - AP = 20 - 8 = 12{\text{ cm}} \cr} $$