Answer
The rectangular lot is 100 feet long and 80 feet wide.
Work Step by Step
Let $x$ be the length and $y$ be the breadth.
$\text{Perimeter}=2x+2y$
Therefore,
$2x+2y=360$ …… (1)
And the total cost of fencing is $20x+8\left( 2y \right)$.
Therefore, according to the question
$\begin{align}
& 20x+8\left( 2y \right)=3280 \\
& 20x+16y=3280
\end{align}$ …… (2)
Consider the steps of the formula:
Step $1$: Multiply $-10$ on both sides of the equation $\left( 1 \right)$ to get:
$-20x-20y=-3600$ …… (3)
Step $2$: Add equation $\left( 3 \right)$ and equation $\left( 2 \right)$ to get:
$\begin{align}
& -20x-20y=-3600 \\
& \underline{20x+16y=3280} \\
& -4y=-320 \\
\end{align}$
Step 3: Divide the above equation by $-4$ to get:
$\begin{align}
& \frac{-4y}{-4}=\frac{-320}{-4} \\
& y=80
\end{align}$
Step 4: Substitute $80$ for $y$ in equation $\left( 1 \right)$ to get:
$\begin{align}
& 2x+2\left( 80 \right)=360 \\
& 2x+160=360
\end{align}$
Step 5: Subtract $160$ from both sides to get:
$\begin{align}
& 2x+160-160=360-160 \\
& 2x=200
\end{align}$
Step 6: Divide the above equation by $2$ to get:
$\begin{align}
& \frac{2x}{2}=\frac{200}{2} \\
& x=100
\end{align}$
Hence, the rectangular lot must be $100$ feet long and $80$ feet wide.
