Answer
The rectangular field has a length of $150$ yards and a width of $50$ yards.
Work Step by Step
We want to find the dimensions of this rectangular field. We have the formula for the perimeter of a rectangle as being:
$$P = 2l + 2w$$
We have the perimeter of the field as $400$ yards.
We set $w$ as the width.
The length is three times as the width, so we can write the following expression to find length in terms of width:
$$l = 3w$$
We can now plug in this expression for length into the formula for perimeter:
$$400 = 2(3w) + 2w$$
Multiply first, according to order of operations:
$$400 = 6w + 2w$$
Add the variables:
$$400 = 8w$$
Divide both sides by $8$ to solve for $w$:
$$w = 50$$
Now that we have the width, we can plug this value into the equation to find the perimeter to find the length:
$$400 = 2l + 2(50)$$
Multiply first:
$$400 = 2l + 100$$
Subtract $100$ from both sides to get the constants on one side of the equation:
$$2l = 300$$
Divide both sides by $2$ to solve for $l$:
$$l = 150$$
The rectangular field has a length of $150$ yards and a width of $50$ yards.
