a.
The perimeter of a figure is given by the sum of the lengths of all sides.
In a rectangle, the perimeter is given by two times the length plus two times the width.
If the length is 3x² + 7x + 9 and the width is 3x + 6, the perimeter is:
[tex]\begin{gathered} P=2L+2W\\ \\ P=2(3x^2+7x+9)+2(3x+6)\\ \\ P=6x^2+14x+18+6x+12\\ \\ P=6x^2+20x+30 \end{gathered}[/tex]So the perimeter is 6x² + 20x + 30.
b.
Now, using x = 5, let's calculate the value of the perimeter:
[tex]\begin{gathered} P=6\cdot5^2+20\operatorname{\cdot}5+30\\ \\ P=6\operatorname{\cdot}25+100+30\\ \\ P=150+130\\ \\ P=280\text{ ft} \end{gathered}[/tex]Therefore the perimeter is 280 ft.