Answer:
The rectangle is 7 km by 14 km. The 14 km dimension is parallel to the river.
Step-by-step explanation:
Let x represent the length of fence parallel to the river. The remaining fence is divided into two equal pieces for the ends of the enclosure. Then (28 -x)/2 will be the length of the side of the rectangle perpendicular to the river.
The total area of the enclosure is the product of length and width:
Area = (x)(28-x)/2
This expression describes a parabola opening downward with zeros at x=0 and x=28. The vertex (maximum) is halfway between those zeros, so is at ...
x = (0 +28)/2 = 14
Area is maximized when the dimension parallel to the river is 14 km and the ends of the enclosure are 7 km.
