Question

A gardener has 1000 feet of fencing to fence in a rectangular garden. One side of the garden is bordered by a river and so it does not need any fencing. river garden e What dimensions would guarantee that the garden has the greatest possible area? shorter side: ft (feet) longer side: ft (feet) ft? (square-feet) greatest possible area:

Answer 1

`\begin{gathered} 2W+L=1000 \\ L=1000-2W \end{gathered}`

Area for a rectangle -> A=WL

`\begin{gathered} A=W\cdot L \\ A=W\cdot(1000-2W) \\ A=1000W-2W^2 \end{gathered}`

Let's derive the equation A

`\begin{gathered} A^(\prime)=1000-4W=0 \\ 4W=1000 \\ W=250ft \end{gathered}`

If W=250, we have

`L=1000-2\cdot250=1000-500=500ft`

Finally, the area

`A=W\cdot L=250\cdot500=125000ft^2`