Final answer:
The width of the playing field is 48 yards and the length is 87 yards.
Step-by-step explanation:
Let's let the width of the field be represented by 'w'.
The length of the field is 9 yards less than double the width, so it can be represented as '2w - 9'.
The perimeter of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width.
Given that the perimeter of the field is 270 yards, we can write the equation as 270 = 2((2w - 9) + w).
Simplifying the equation, we have 270 = 2(3w - 9), which becomes 270 = 6w - 18 when we distribute 2.
Adding 18 to both sides of the equation, we get 288 = 6w.
Dividing both sides of the equation by 6, we find that w = 48.
So, the width of the playing field is 48 yards.
To find the length, we substitute the value of w back into the equation for the length: l = 2(48) - 9 = 87.
Therefore, the dimensions of the playing field are: Width = 48 yards, Length = 87 yards.