# Just An Inscribed Square

Calculus Level 3

A square $$PQRS$$ is inscribed inside a square $$ABCD$$, with $$P$$ on $$AB$$. If $$P$$ is uniformly distributed along side $$AB$$, the expected area of $$PQRS$$ is $$24\text{ unit}^2$$. What is the side length of square $$ABCD$$ (in $$\text{unit}$$)?