Answer
The length of the field is $200$ yards and the width is $50$ yards.
Work Step by Step
We know that the perimeter of a rectangle can be given by the following formula:
$$P = 2l + 2w$$
We know from the problem that the perimeter is $500$ yards and that the length of the field is four times greater than its width. We can set up an equation as follows:
$$500 = 2(4w) + 2w$$
We can simplify this equation:
$$8w + 2w = 500$$
Combine like terms:
$$10w = 500$$
Solve for $w$ by dividing each side by $10$:
$$w = 50$$
We know that the length, $l$, is four times greater than the width; therefore, we can find length with the following equation:
$$l = 4(50)$$
Solve for $l$:
$$l = 200$$
The length of the field is $200$ yards and the width is $50$ yards.
