Answer: Option A.
Step-by-step explanation:
1. The formula for caculate the perimeter of a rectangle is:
[tex]P=2l+2w[/tex]
Where [tex]l[/tex] is the lenght and [tex]w[/tex] is the width.
2. You must substitute the expression of the perimeter and the expression of the length given in the problem, into the equation and solve for the width. Therefore, you obtain that the width is:
[tex]6x^{2}+46x+68=2(2x^{2}+18x+28)+2w\\6x^{2}+46x+68=4x^{2}+36x+56+2w\\2w=6x^{2}+46x+68-4x^{2}-36x-56\\w=\frac{2x^{2}+10x+12}{2}\\w=x^{2}+5x+6[/tex]
3. The answer is the option A.
