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
