Answer
The width of the ribbon in inches is $1.5$.
Work Step by Step
We have the formula for the area of the ribbon:
$A=lw$
Plug in values:
$24=(2x+13)x$
$2x^2+13x=24$
$2x^2+13x-24=0$
$(2x-3)(x+8)=0$
$(2x-3)=0$ or $x+8=0$
$x=\frac{3}{2}$ or $x=-8$
The width cannot be negative.
Therefore, the width of the ribbon in inches is $1.5$.