A new youth activity center is being built in pagosa springs. The perimeter of the rectangular playing field is 328 yards. The length of the field is 4 yards less than double the width. What are the dimensions of the playing field?

Width: 56 yards, Length: 108 yards

Step-by-step explanation:

What we know:

- Perimeter is 328 yards

- The length is 4 less than double the width

In this answer, I will use w as the variable for width.

Find the equation for the length.

The length of the field is double the width, 2w, minus 4.

We get: 2w - 4

A rectangle has four sides, two for width, two for length. So now we need to add width to width and length to length

Length: (2w - 4) + (2w - 4) = 4w - 8

Width: w + w = 2w

To find perimeter, you need to add all sides. So now we add our length and width

4w - 8 + 2w = 6w - 8

Now that we have our final equation, we need to solve for w.

6w - 8 = 328

Add 8 to both sides.

6w - 8 + 8 = 328 + 8

Combine like terms.

6w = 336

Divide 6 from both sides.

w = 56

The width is 56, now that we have solved w, we can plug it into our length equation

2(56) - 4 = 108

The length is 108.

56 yards x 108 yards (width x length)

To check your work, you can easily add up all the sides and see if it matches the perimeter given.

108 + 108 + 56 + 56 = 328

I hope this helped!