Answer
The length of the rectangular field is $120$ yards and the width is $24$ yards.
Work Step by Step
We know that the formula for the perimeter of a rectangle is:
$$P = 2l + 2w$$
We know from the problem that the perimeter is $288$ yards and the length is five times the width, $w$, so we can express the length in terms of width as follows:
$$l = 5w$$
We can now put together the equation using what we know from the problem:
$$288 = 2(5w) + 2w$$
We can now simplify the equation:
$$10w + 2w = 288$$
Combine like terms:
$$12w = 288$$
Solve for $w$ by dividing both sides by $12$:
$$w = 24$$
We now plug $24$ back into the equation to find $l$. If $l = 5w$, then:
$$l = 5(24)$$
$$l = 120$$
The length of the rectangular field is $120$ yards and the width is $24$ yards.
