Algebra shape question: find area of polygon, given some side measurements

[bluefrog]

The shape below has an area of $$44 m^2$$.
Find the value of $$x$$ ?



I tried as follows:
$$(2x \times x) + ( x \times [ (x+3)-x )] = 44 \\ \Rightarrow 2x^2 + 3x = 44 \\ \Rightarrow (x-4)(2x+11)=0 \\ \Rightarrow x = 4 \text{ since length is positive}$$I split the shape in two, a larger bottom rectangle, and a smaller top rectangle.

However the answer given as


Can anybody help with pointing out what I did wrong, as I do not understand the answer given.

Thanks

 

[stapel]

That's got to be a solution to a different exercise. Their area equation says that the room has a floorspace of 50 square meters, not 44.

I get your answer, by the way. (And *thank you* for showing your work so nicely!)

Eliz.