The problem states that a rectangular playing field has a perimeter of 538 yards. The length of the field is 6 yards less than quadruple the width. We are asked to find the dimensions (width and length) of the playing field.

1. Problem Description

The problem states that a rectangular playing field has a perimeter of 538 yards. The length of the field is 6 yards less than quadruple the width. We are asked to find the dimensions (width and length) of the playing field.

2. Solution Steps

Let $w$ be the width of the rectangular field, and $l$ be the length of the rectangular field. We are given that the perimeter is 538 yards, so

$$2l + 2w = 538$$

We are also given that the length is 6 yards less than quadruple the width, so

$$l = 4w - 6$$

Now we have a system of two equations with two variables:

$$2l + 2w = 538$$

$$l = 4w - 6$$

We can substitute the second equation into the first equation to solve for $w$:

$$2(4w - 6) + 2w = 538$$

$$8w - 12 + 2w = 538$$

$$10w - 12 = 538$$

$$10w = 550$$

$$w = 55$$

Now that we have the width, we can find the length:

$$l = 4w - 6 = 4(55) - 6 = 220 - 6 = 214$$

So the width is 55 yards and the length is 214 yards.

3. Final Answer

The width is 55 yards.

The length is 214 yards.