# Square trapped in a triangle

Geometry Level 3

$$ABC$$ 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 $$PQRS$$.

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