Just An Inscribed Square

Calculus Level 4

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 \(\text{unit}\))?

Give your answer to 1 decimal place.

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