Answer
The width of the rectangular lot is $70$ yards and the length is $130$ yards.
Work Step by Step
The formula for the perimeter of a rectangle is given by the following formula:
$$P = 2l + 2w$$
From the problem, we know that the perimeter of the rectangular lot is $400$ yards and that the length $l$ of the lot is $2w - 10$. We can now devise an equation that incorporates all of this information:
$$400 = 2(2w - 10) + 2w$$
First, we distribut what is in the parentheses:
$$400 = 4w - 20 + 2w$$
Simplify by combining like terms:
$$400 = 6w - 20$$
Add $20$ to each side of the equation to isolate the constants on one side of the equation:
$$6w = 420$$
Divide each side of the equation by $6$ to isolate $w$:
$$w = 70$$
We can now substitute $70$ in for $w$ to find the length $l$:
$$l = 2(70) - 10$$
Multiply first, according to order of operations:
$$l = 140 - 10$$
Subtract to solve for $l$:
$$l = 130$$
The width of the rectangular lot is $70$ yards and the length is $130$ yards.
