# Problem of the Week Problem E A Square in a Triangle

In $$\triangle ABC$$, there is a right angle at $$B$$ and the length of $$BC$$ is twice the length of $$AB$$. In other words, $$BC=2AB$$.

Square $$DEFB$$ is drawn inside $$\triangle ABC$$ so that vertex $$D$$ is somewhere on $$AB$$ between $$A$$ and $$B$$, vertex $$E$$ is somewhere on $$AC$$ between $$A$$ and $$C$$, vertex $$F$$ is somewhere on $$BC$$ between $$B$$ and $$C$$, and the final vertex is at $$B$$.

Square $$DEFB$$ is called an inscribed square. Determine the ratio of the area of the inscribed square $$DEFB$$ to the area of $$\triangle ABC$$.