Farmer Ed has 2,500 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
The largest area that can be enclosed


Answer 1

The largest area that can be enclosed is  781250 m²

Area of rectangle
  • area = lw


l = length

w = width

The farmer wants to enclose a rectangular plot that borders a river. He is not fencing the side along the river. Therefore,

perimeter = l + 2w

l = 2500 - 2w


area = (2500 - 2w)w

(2500 - 2w)w = 0

w = 0 or 1250

average = 1250 / 2 = 625 meters

Hence, the max area is at w = 625 meters


l = 2500 - 2(625) = 1250

length = 1250 meters

width = 625 meter


area = 1250 × 625 = 781250 m²

Therefore, the largest area that can be enclosed is  781250 m²

learn more on rectangle

Answer 2


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

Step-by-step explanation:

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