Answer:
Step-by-step explanation:
The maximum area polygon for a given perimeter is a regular polygon. The regular 4-sided polygon is the square. Each side length will be ...
(1600 yd)/4 = 400 yd
The area will be (400 yd)² = 160,000 yd².
The maximum area Diana can enclose is a square 400 yards on each side, for a total of 160,000 square yards.
_____
On dimension can be represented by x, and the other by y. The sum of the two dimensions will be half the perimeter, so we have ...
y = 800 -x
The area is then ...
A = xy = x(800 -x)
This equation describes a parabola that opens downward. It has zeros at x=0 and x=800. The vertex (maximum area) is on the line of symmetry halfway between those values, at x = 400. Then y = 800 -400 = 400, and the rectangle is a square.
