Question

The perimeter of the rectangular playing field is 254 yards. the length of the field is 8 yards less than double the width. what are the dimensions

Answer 1

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,

`\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=(270)/(6) \\ Calculate \\ W=45\text{ }yards \end{gathered}`

Next, we plug in w=45 into L = 2W-8:

`\begin{gathered} L=2W-8 \\ L=2(45)-8 \\ Simplify \\ L=82\text{ yards} \end{gathered}`

Therefore, the dimensions are:

Length=82 yards

Width = 45 yards