A rough sketch of the rectangular plot is
The perimeter of the rectangle is given by the formula:
[tex]P=2l+2w[/tex]
Where,
and,
i
The perimeter is 320, so we can write:
[tex]\begin{gathered} P=2l+2w \\ 2l+2w=320 \\ 2(l+w)=320 \\ l+w=160 \end{gathered}[/tex]
Total fencing cost $3120 and this is 1 length side and 2 width side.
The fencing on length side is $24 per foot and width side is $4 per foot.
e can write an equation:
[tex]\begin{gathered} 24l+2(4w)=3120 \\ 24l+8w=3120 \end{gathered}[/tex]
Now, we have to solve the 2 simultaneous equations,
[tex]\begin{gathered} l+w=160 \\ 24l+8w=3120 \end{gathered}[/tex]
Let's solve with elimination >>>>
[tex]\begin{gathered} l+w=160 \\ 24l+8w=3120 \\ ----------- \\ -8\times(l+w=160) \\ 24l+8w=3120 \\ ------------ \\ -8l-8w=-1280 \\ 24l+8w=3120 \\ _{\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\text{.}} \\ 16l=1840 \\ l=\frac{1840}{16} \\ l=115 \end{gathered}[/tex]
We can substitute this value of "l" into the first equation and solve for "w". This is shown below:
[tex]\begin{gathered} l+w=160 \\ 115+w=160 \\ w=160-115 \\ w=45 \end{gathered}[/tex]
Thus,
Answer
The Longer Dimension is 115 feet
The Shorter Dimension is 45 feet
