# Areas Inside a Rectangle

Geometry Level 4

$$ABCD$$ is a rectangle with point $$E$$ on line segment $$AB$$ and point $$F$$ on line segment $$BC$$ such that $$[ADE] = 7$$, $$[BEF] = 11$$ and $$[DCF] = 9$$. Then $$[DEF] = a\sqrt{b}$$, where $$a$$ and $$b$$ are integers and $$b$$ is not a multiple of the square of any prime. What is the value of $$a + b$$?

Details and assumptions

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

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