Question

Farmer Ed has 1.000 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

Answer:

  1000 m of fence can make a 3-sided enclosure of 125,000 m²

Step-by-step explanation:

Let x represent the length of fence parallel to the river. Then the perpendicular dimension is ...

  width = (1000 -x)/2

and the enclosed area is ...

  area = length×width = (x)(1000 -x)/2

This describes a downward-opening parabola with zeros at x=0 and x=1000. The vertex (maximum) is halfway between, at x=500.

Then the maximum area is ...

  area = (500)(1000 -500)/2 = 125,000 . . . . square meters