Let's call the width [tex]w[/tex] and the length [tex]l[/tex] based on this, we can make two equations based on the first and second sentences in the problem.
[tex]w = l + 2[/tex]
[tex]2l + 2w = 182[/tex]
If we substitute [tex]l + 2[/tex] for [tex]w[/tex] into the second equation, we can make the following:
[tex]2l + 2(l + 2) = 182[/tex]
[tex]2l + 2l + 4 = 182[/tex]
[tex]4l + 4 = 182[/tex]
[tex]4l = 178[/tex]
[tex]l = \dfrac{178}{4} = \dfrac{89}{2}[/tex]
Now, let's find [tex]w[/tex]:
[tex]w = l + 2 = \dfrac{89}{2} + 2 = \dfrac{93}{2}[/tex]
The length of the rectangle is [tex]\boxed{\dfrac{89}{2} \,\textrm{ft}}[/tex] and the width of the rectangle is [tex]\boxed{\dfrac{93}{2} \,\textrm{ft}}[/tex].
