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?
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.
Let's assume that the width of the playing field is "W" yards.
According to the given information, the length of the field is 6 yards less than quadruple the width. Therefore, the length of the field can be expressed as (4W - 6) yards.
The formula for the perimeter of a rectangle is P = 2L + 2W, where P represents the perimeter, L represents the length, and W represents the width.
Using the formula for the perimeter, we can write the equation:
578 = 2(4W - 6) + 2W
Now, let's simplify and solve this equation step-by-step:
578 = 8W - 12 + 2W
578 = 10W - 12
578 + 12 = 10W
590 = 10W
W = 590/10
W = 59
Thus, the width of the playing field is 59 yards.
To find the length of the playing field, we can substitute the width value into the expression for the length:
Length = 4W - 6
Length = 4(59) - 6
Length = 236 - 6
Length = 230
Therefore, the dimensions of the playing field are a width of 59 yards and a length of 230 yards.
To find the dimensions of the playing field, we need to set up an equation based on the given information.
Let's assume that the width of the field is represented by the variable 'w'.
According to the problem, the length of the field is 6 yards less than quadruple the width.
So, the length of the field would be 4w - 6.
Now, the formula for the perimeter of a rectangle is 2(length + width).
Since we know the perimeter of the playing field is 578 yards, we can set up an equation:
2(4w - 6 + w) = 578
Simplifying the equation:
2(5w - 6) = 578
10w - 12 = 578
10w = 578 + 12
10w = 590
w = 590 / 10
w = 59
Now that we know the width (w) is 59 yards, we can substitute this value back into our expression for the length to find the length of the field:
Length = 4w - 6
Length = 4(59) - 6
Length = 236 - 6
Length = 230
So, the dimensions of the playing field are 230 yards by 59 yards.