A new Outdoor Recreation Center is being built in Erie. The perimeter of the rectangular playing field is "342" yards. The length of the field is 6 yards less than double the width. What are the dimensions of the playing field?
Let's call the width of the playing field "x".
According to the problem, the length of the field is 6 yards less than double the width. So, the length is 2x - 6.
The perimeter of a rectangle is given by the formula: P = 2*(length + width)
Since the perimeter of the playing field is 342 yards, we can write the equation: 342 = 2*(2x - 6 + x)
Expanding the equation, we get: 342 = 2*(3x - 6)
Now, let's solve for x:
342 = 6x - 12
6x = 342 + 12
6x = 354
x = 354/6
x ≈ 59
So, the width of the playing field is approximately 59 yards.
Now, using this value, let's find the length of the field:
Length = 2x - 6
Length = 2*59 - 6
Length = 118 - 6
Length = 112
So, the dimensions of the playing field are approximately 112 yards by 59 yards.
Let's say the width of the playing field is "x" yards.
According to the given information, the length of the field is 6 yards less than double the width, which means it is (2x - 6) yards.
The perimeter of a rectangle is calculated by adding the lengths of all four sides. In this case, we have two lengths and two widths, so the equation becomes:
2x + 2(2x - 6) = 342
Simplifying the equation, we have:
2x + 4x - 12 = 342
6x - 12 = 342
Adding 12 to both sides:
6x = 342 + 12
6x = 354
Dividing both sides by 6:
x = 354 / 6
x = 59
So, the width of the playing field is 59 yards.
The length of the field can be found by substituting the value of x back into the equation for the length:
2x - 6 = 2(59) - 6
2x - 6 = 118 - 6
2x - 6 = 112
Therefore, the length of the playing field is 112 yards.
In conclusion, the dimensions of the playing field are 59 yards (width) by 112 yards (length).
To find the dimensions of the playing field, we can set up an equation based on the given information.
Let's assume the width of the playing field as "w" yards.
According to the problem, the length of the playing field is 6 yards less than double the width, which can be written as (2w - 6) yards.
The perimeter of a rectangle is given by the formula:
Perimeter = 2(length + width)
Given that the perimeter of the playing field is 342 yards, we can write the equation as:
342 = 2((2w - 6) + w)
To find the value of "w," we solve the equation:
342 = 2(3w - 6)
342 = 6w - 12
354 = 6w
w = 59
So, the width of the playing field is 59 yards.
Now, we can substitute the value of the width back into the expression for the length:
Length = 2w - 6 = 2(59) - 6 = 112 - 6 = 106
Therefore, the dimensions of the playing field are 106 yards by 59 yards.