Farmer Ed has7500 meters of fencing, and wants to enclose a rectangular plot that borders on a river.

Question

Farmer Ed has7500 meters of fencing, and wants to enclose a rectangular plot that borders on a river. If Farmer Ed does not fence the side along the river, what is the largest area that can be enclosEd?

Answer 1

Because it is a rectangle, the area is expressed as A = xy, or length times width.

Because it is next to the river, he only needs to fence three sides, so F = x + 2y.

Knowing the amount of fencing available is 7500m, we get:

 

7500 = x + 2y        solve for x

x = 7500 - 2y         substitute into the area equation

A = (7500 - 2y)y     distribute

A = -2y² +7500y

 

You can see that this is a parabola which opens down, meaning that the point of maximum area will be at the vertex, y = -b/2a = -7500/[2(-2)] = 1875

 

x = 7500 - 2(1875) = 3750

 

A = 3750(1875)  = 7,031,250 m²