Question

You need to enclose an area of 300 square feet with fence. If the area is rectangular, what is the least amount of fence you need?

Answer 1

Given

An enclose an area of 300 square feet with fence. If the area is rectangular, what is the least amount of fence

Solution

Then perimeter

`Perimeter=2(x+(300)/(x))`
`\begin{gathered} (dp)/(dx)=2(1-(300)/(x^2))=0 \\ \\ 1-(300)/(x^2)=0 \\ \\ 1=(300)/(x^2) \\ \\ x^2=300 \\ x=√(300) \end{gathered}`

Now substitute x into the perimeter

`\begin{gathered} Perimeter=2(√(300)+(300)/(√(300))) \\ perimeter\text{ =amount} \\ Amount=2(√(300)+(300)/(√(300))) \\ Amount=40√(3) \\ Amount=69.28203 \end{gathered}`

The least amount of fence 69.28203ft