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8 December, 15:44

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?

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  1. 8 December, 19:38
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    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.
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