Square trapped in a triangle

Geometry Level 3

ABCABC is an isosceles triangle with AB=ACAB = AC and BC=48BC = 48. DEFGDEFG is a square inscribed in triangle ABCABC such that vertices DD and EE lie on ABAB and ACAC respectively, while vertices FF and GG lie on BCBC. If [ADE]=24[ADE] = 24, what is the side length of the square DEFGDEFG?

Details and assumptions

[PQRS][PQRS] denotes the area of figure PQRSPQRS.

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