Distance to side

$ABC$ is a right triangle with $m\angle C=90^{\circ}$ . $AC=10\text{ units}^2$ and $BC=24\text{ units}^2$ . Point $P$ is located inside $ABC$ such that the distance from $P$ to $AB$ is twice the distance from $P$ to $AC$ , and the distance from $P$ to $AC$ is twice the distance from $P$ to $BC$ . In $\text{units}^2$ , what is the distance from $P$ to $AB$ ?

Express your answer as a decimal to the nearest hundredth.