A new youth sports center is being built in pagosa springs. The permitted of the rectangular playing field is 524 yards. The length of the field is 8 yards lass then quadruple the with. What are the dimensions of the playing field?

Length = 208 yards

Width = 54 yards

Step-by-step explanation:

Let the length of the field be "x" yards and the width be "y" yards. Its given that the length is 8 less than quadruple (4 times) the width. So x is 8 less than 4y. We can write this in equation as:

x = 4y - 8 Equation 1

Perimeter of the field is given to be 524 yards. Since, the field is rectangular, its perimeter is calculated as:

Perimeter = 2 (Length + Width)

Using the values, we get:

2 (x + y) = 524 Equation 2

Substituting the value of x from Equation 1 into Equation 2, we get:

2 (4y - 8 + y) = 524

2 (5y - 8) = 524

5y - 8 = 524/2

5y - 8 = 262

5y = 262 + 8

5y = 270

y = 54 yards

Substituting the value of y in Equation 1, we get:

x = 4y - 8 = 4 (54) - 8 = 208 yards

Thus, the length of the playing field is 208 yards and its width is 54 yards.