Answer
The rectangle has a length of $150$ yards and a width of $50$ yards.
Work Step by Step
We know that the perimeter is given by the formula:
$$P = 2l + 2w$$
where $P$ is the perimeter of the rectangle, $l$ is the measure of its length, and $w$ is the measure of its width.
In this problem, we set $w$ as the width. The length is three times the width, so $l = 3w$.
We plug in what we have for $w$ and $l$ into the formula for perimeter, where we have $P = 400$:
$$400 = 2(3w) + 2w$$
We can now solve for $w$, the width.
Let's multiply first:
$$400 = 6w + 2w$$
Add the variable terms together:
$$400 = 8w$$
Divide both sides by $8$ to solve for $w$:
$$w = 50$$
Now that we have the measure for width, we can substitute $50$ for $w$ into the original equation:
$$400 = 2l + 2(50)$$
Multiply:
$$400 = 2l + 100$$
Subtract $100$ from both sides to isolate the variable on one side and the constant terms on the other:
$$300 = 2l$$
Divide both sides by $2$ to solve for $l$:
$$l = 150$$
The rectangle has a length of $150$ yards and a width of $50$ yards.
