Final answer:
The width of the field is 56 yards and the length is 104 yards, determined by setting up linear equations based on the given perimeter and the relationship between the length and width of the field.
Step-by-step explanation:
The student is asking for help to find the dimensions of a field where the perimeter is given as 320 yards and the length of the field is described as 8 yards less than double the width. This problem involves setting up and solving linear equations to find the dimensions of a rectangle.
Let width be represented as 'w' and length as 'l'. From the problem, we can write the equation for the perimeter (P) of the rectangle (field) as P = 2l + 2w. Since the perimeter is 320 yards, we therefore have 320 = 2l + 2w. According to the problem, the length is 8 yards less than double the width, which gives us the equation l = 2w - 8.
We can substitute the second equation into the first to get 320 = 2(2w - 8) + 2w, which simplifies to 320 = 4w - 16 + 2w. Solving this equation, we get 6w = 320 + 16, hence w = 56 yards. Substituting w back into l = 2w - 8, we find l = 2(56) - 8 = 112 - 8 = 104 yards. Thus, the width of the field is 56 yards, and the length is 104 yards.