A new Youth Sports Center is being built in Hadleyville. The perimeter of the rectangular playing field is 578 yards. The length of the field is 6 yards less than quadruple the width . What are the dimensions of the playing field?

Answer 1

Let's assume the width of the field is x yards.
According to the given information, the length of the field is 6 less than four times the width, which can be written as 4x - 6 yards.
The perimeter is the sum of all sides of a rectangle, which can be calculated using the formula: P = 2(length + width).
In this case, the perimeter is 578 yards, so we can write the equation as:
578 = 2(4x - 6 + x)
Now, let's simplify and solve the equation:
578 = 2(5x - 6)
578 = 10x - 12
578 + 12 = 10x
590 = 10x
x = 590/10
x = 59
So, the width of the field is 59 yards.
The length of the field is 4(59) - 6 = 236 - 6 = 230 yards.
Therefore, the dimensions of the playing field are 59 yards by 230 yards.