The figure depicts two vessels, P and Q, each having sides that are tilted at $45^{\circ}$. As illustrated, vessel P widens upwards while vessel Q narrows upwards. Each vessel contains a liquid, and the liquids are at the same depth. The liquid in vessel P has twice the density of the liquid in vessel Q. Find the ratio $\dfrac{\text{pressure due to the liquid on the base of P}}{\text{pressure due to the liquid on the base of Q}}$?
- A$\dfrac{2}{1}$
- B$\dfrac{\sqrt{2}}{1}$
- C$\dfrac{1}{\sqrt{2}}$
- D$\dfrac{1}{2}$