P, 2P, 3P and 4P are the magnitudes of forces act along the sides of a square ABCD in cyclic order. The magnitude of their resultant force is

Resultant force always x axis

$\Rightarrow {\overrightarrow{P}}_x=-3\text{P}\hat{i}+\text{P}\hat{i}$  $=-2\text{P}\hat{i}$

Resultant force always y axis

$\Rightarrow {\overrightarrow{P}}_y=2\text{P}\hat{j}-4\text{P}\hat{j}$  $=-2\text{P}\hat{j}$

Magnitude of resultant of ${\overrightarrow{P}}_x$ and${\overrightarrow{P}}_y$

$=\sqrt{P_x^2+P_y^2}$

$=\sqrt{{\left(2\text{P}\right)}^2+{\left(2\text{P}\right)}^2}$

$=\sqrt{2\times {\left(2\text{P}\right)}^2}=2\text{P}\sqrt{2}$

$=2\sqrt{2}\text{P}$