Answer
$ 8$ inches
Work Step by Step
The perimeter is the sum of the sides' lengths
$P=\displaystyle \frac{4x+9}{x+4}+\frac{7}{x+4}+\frac{4x+9}{x+4}+\frac{7}{x+4}$
To add/subtract rational expressions with the same denominator,
add/subtract numerators and place the sum/difference over the common denominator.
$P=\displaystyle \frac{4x+9+7+4x+9+7}{x+4}$
$=\displaystyle \frac{8x+32}{x+4}$
$=\displaystyle \frac{8(x+4)}{(x+4)}$
... common factors cancel,
=$ 8$ inches
