Answer
The Width of the room is $12ft$
Work Step by Step
$\underline{\textbf{Givens:}}$
$Area=228ft2$
$Width=x$
$Length(L)=x+7ft$
$We know Area of a Rectangle =L\times W$
i.e
$x(x+7)=228$
$\Rightarrow x^2+7x=228$
$\Rightarrow x^2+7x-228=0$
By Factoring
$\Rightarrow (x-12)(x+19)=0$
$\Rightarrow x=12$ or $x=-19\hspace{0.3cm} {\color{red}{Rejected}}$
Width can not be expressed with a negative measurement.
$Width = 12ft$
$Length= 12+7=19ft$
