Final answer:
The dimensions of a rectangular field with a perimeter of 450 yards, where the length is four times the width, are a width of 45 yards and a length of 180 yards.
Step-by-step explanation:
To determine the dimensions of a rectangular field where the length is four times the width and the perimeter is 450 yards, we first need to set up two equations based on the information given. Let's denote the width of the field as w and the length as 4w (since the length is four times the width). The perimeter P of a rectangle is given by P = 2(length + width). Substituting the known values, we get 450 yards = 2(4w + w).
Simplifying the equation gives us 450 yards = 2(5w), which further simplifies to 450 yards = 10w. Dividing both sides by 10 yields w = 45 yards. So the width is 45 yards and the length, being four times the width, is 180 yards.
The dimensions of the field are therefore a width of 45 yards and a length of 180 yards.