Answer :
Given the word problem, we can deduce the following information:
Perimeter of the rectangle = 254 yards
L = 2W-8
where:
W=width
L=Length
To determine the dimensions, we first note that the formula for the rectangle's perimeter is:
P=2(L+W)
where:
P=Perimeter
L=Length
W=Width
So,
[tex]\begin{gathered} P=2\left(L+W\right) \\ 254=2(2W-8+W) \\ Simplify\text{ and rearrange} \\ 254=2(3W-8) \\ 254=6W-16 \\ 6W=254+16 \\ 6W=270 \\ W=\frac{270}{6} \\ Calculate \\ W=45\text{ }yards \end{gathered}[/tex]Next, we plug in w=45 into L = 2W-8:
[tex]\begin{gathered} L=2W-8 \\ L=2(45)-8 \\ Simplify \\ L=82\text{ yards} \end{gathered}[/tex]Therefore, the dimensions are:
Length=82 yards
Width = 45 yards