Question

Hello I need help for my study guide :(

Answer 1

A rough sketch of the rectangular plot is

The perimeter of the rectangle is given by the formula:

`P=2l+2w`

Where,

and,

i

The perimeter is 320, so we can write:

`\begin{gathered} P=2l+2w \\ 2l+2w=320 \\ 2(l+w)=320 \\ l+w=160 \end{gathered}`

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:

`\begin{gathered} 24l+2(4w)=3120 \\ 24l+8w=3120 \end{gathered}`

Now, we have to solve the 2 simultaneous equations,

`\begin{gathered} l+w=160 \\ 24l+8w=3120 \end{gathered}`

Let's solve with elimination >>>>

`\begin{gathered} l+w=160 \\ 24l+8w=3120 \\ ----------- \\ -8*(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=(1840)/(16) \\ l=115 \end{gathered}`

We can substitute this value of "l" into the first equation and solve for "w". This is shown below:

`\begin{gathered} l+w=160 \\ 115+w=160 \\ w=160-115 \\ w=45 \end{gathered}`

Thus,

Answer

The Longer Dimension is 115 feet

The Shorter Dimension is 45 feet