Square trapped in a triangle
\(ABC\) is an isosceles triangle with \(AB = AC\) and \(BC = 48\). \(DEFG\) is a square inscribed in triangle \(ABC\) such that vertices \(D\) and \(E\) lie on \(AB\) and \(AC\) respectively, while vertices \(F\) and \(G\) lie on \(BC\). If \([ADE] = 24\), what is the side length of the square \(DEFG\)?
Details and assumptions
\([PQRS]\) denotes the area of figure \(PQRS\).