A new Youth Sports Center os being built in Hadleyville. The perimeter of the rectangular playing field is 462 yards. The length of the field is 9 yards less than quadrupled the width. What are the dimensions of the playing field?
Let's assume the width of the playing field is x yards.
According to the information given, the length of the field is 9 yards less than quadrupled the width, which is 4x - 9 yards.
The perimeter of a rectangle is given by the formula: P = 2(l + w).
Plugging in the given information, we can write the equation as follows:
462 = 2(4x - 9 + x)
462 = 2(5x - 9)
462 = 10x - 18
10x = 480
x = 480/10
x = 48
So, the width of the field is 48 yards.
The length of the field is 4x - 9 = 4(48) - 9 = 192 - 9 = 183 yards.
Therefore, the dimensions of the playing field are 48 yards by 183 yards.
Let's solve this step by step.
Let's assume the width of the field is "w" yards.
According to the problem, the length of the field is 9 yards less than quadrupled the width, which can be written as (4w - 9) yards.
The perimeter of a rectangle is given by the formula P = 2(l + w), where P is the perimeter, l is the length, and w is the width.
Given that the perimeter of the playing field is 462 yards, we can write the equation as:
462 = 2((4w - 9) + w)
Now, we can simplify the equation and solve for 'w':
462 = 2(5w - 9)
462 = 10w - 18
10w = 462 + 18
10w = 480
w = 480/10
w = 48
Therefore, the width of the field is 48 yards.
To find the length of the field, we can substitute the value of 'w' into the equation for the length:
Length = 4w - 9
Length = 4(48) - 9
Length = 192 - 9
Length = 183
Therefore, the length of the field is 183 yards.
So, the dimensions of the playing field are 48 yards by 183 yards.
To find the dimensions of the playing field, we can set up an equation using the given information.
Let's assume the width of the field is "x" yards.
According to the problem, the length of the field is 9 yards less than quadrupled the width. In other words, the length is (4x - 9) yards.
The perimeter of a rectangle is given by the formula: Perimeter = 2 * (length + width).
Based on the information given, we can write the equation as:
2 * (4x - 9 + x) = 462
Simplifying the equation, we have:
2 * (5x - 9) = 462
10x - 18 = 462
10x = 462 + 18
10x = 480
Dividing both sides by 10, we get:
x = 48
Now, we can substitute the value of "x" back into the equation to find the length:
Length = 4x - 9
= 4 * 48 - 9
= 192 - 9
= 183
Therefore, the width of the field is 48 yards, and the length of the field is 183 yards.