Answer
The length of the field is $360$ feet and the width is $160$.
Work Step by Step
The perimeter of a rectangle is given by the formula:
$$P = 2l + 2w$$
We know from the problem that the perimeter is $1040$ feet, so we can plug that into the equation:
$$1040 = 2l + 2w$$
We also know that the length is $200$ feet more than the width, $w$. We can plug this into the equation:
$$1040 = 2(w + 200) + 2w$$
We simplify the equation:
$$2w + 400 + 2w = 1040$$
We combine like terms:
$$4w + 400 = 1040$$
We subtract $400$ from both sides:
$$4w = 640$$
We divide both sides by $4$ to isolate $w$:
$$w = 160$$
If we know that the width $w$ is $160$ feet, we know that the length $l$ is $200$ feet more than the width, so we have the length as:
$$l = w + 200$$
We plug in $160$ for $w$:
$$l = 160 + 200$$
We add the right-hand side of the equation:
$$l = 360$$
The length of the field is $360$ feet and the width is $160$ feet.
