The width of the rectangular field is 56 yards, and its length is 216 yards.
In the question, we are given that a new youth sports center is being built in Junction City. The perimeter of the rectangular playing field is 544 yards. The length of the field is 8 yards less than quadruple the width.
We are asked to find the width and the length of the field.
We assume the width of the rectangular field to be x yards.
Thus, we have the width of the rectangular field = x yards.
The length of the rectangular field = 8 yards less than quadruple the width = 4x - 8 yards.
The perimeter of a rectangle is given as 2(length + width).
Thus, the perimeter of the rectangular field can be shown as 2{(4x - 8) + x} yards.
But, the perimeter of the rectangular field is given to be 544 yards.
Thus, equating the two values, we get a linear equation:
2{(4x - 8) + x} = 544.
This equation can be solved as:
2{(4x - 8) + x} = 544,
or, 5x - 8 = 272,
or, 5x = 280,
or, x = 56.
Thus, we have the
width = x yards = 56 yards, and the
length = 4x - 8 yards = 4*56 - 8 yards = 216 yards.
Thus, the width of the rectangular field is 56 yards, and its length is 216 yards.
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