Alex has 360 yards of fencing to enclose a rectangular area. Find the dimensions of the rectangle that maximize the enclosed area. What is the maximum area?

90 yd by 90 yd (square) 8100 yd²

Step-by-step explanation:

When the perimeter of the rectangle is 360 yd, the sum of the lengths of two adjacent sides is 180 yd. If x is the length of one side of the rectangle, then the adjacent side is (180-x). The area is the product of these lengths,

area = x (180 - x)

This describes a downward-opening parabola with zeros at x=0 and x=180. The vertex (maximum) of the parabola is halfway between, at x=90. The adjacent sides of the maximum-area rectangle are the same length: the rectangle is a square with sides 90 yards each.

The area is (90 yd) ² = 8100 yd².