Diana has 1600 yards of fencing to enclose a rectangular area. Find the dimensions of the rectangle that maximize the enclosed area. What is the maximum area ?

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.

no solution

step-by-step explanation:

there is not enough information in the problem to solve.