A rectangular plot of farmland will be bounded on one side by a river and on the other three sides by a single-strand electric fence. With 1100 m of wire at your disposal, what is the largest area you can enclose, and what are its dimensions?

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walber000 walber000 · Answer 1 · 2020-06-27T03:35:17+02:00

Answer:

Length = 550 m

Width = 275 m

Area = 151,250 m2

Step-by-step explanation:

One side of the farmland is bounded by the river, so the perimeter we will need to enclose is:

[tex]Perimeter = Length + 2*Width = 1100\ m[/tex]

And the area of the farmland is given by:

[tex]Area = Length * Width[/tex]

From the Perimeter equation, we have that:

[tex]Length = 1100 - 2*Width[/tex]

Using this in the area equation, we have:

[tex]Area = (1100 - 2*Width) * Width[/tex]

[tex]Area = 1100*Width - 2*Width^2[/tex]

Now, to find the largest area, we need to find the vertex of this quadratic equation, and we can do that using the formula:

[tex]Width = -b/2a[/tex]

[tex]Width = -1100/(-4)[/tex]

[tex]Width = 275\ m[/tex]

This width will give the maximum area of the farmland. Now, finding the length and the maximum area:

[tex]Length = 1100 - 2*Width = 1100 - 550 = 550\ m[/tex]

[tex]Area = Length * Width = 550 * 275 = 151250\ m2[/tex]