Question

A rectangular area is to be fenced in with 600 feet of chicken wire. find the maximum area that can be enclosed.

Answer 1

600 ft is the perimeter of the area.
the area of the area is max when it's a square
the length of the square is 600/4 = 150
so the max area that can be enclosed is:
150×150 = 22500 ft square

Answer 2

The maximum area that can be enclosed is 22500 feet²

A rectangle is a quadrilateral in which opposite sides are equal and parallel to each other.

Let x represent the length and y represent the width. Hence:

perimeter = 2(length + width)

600 = 2(x + y)

300 = x + y

y = 300 - x

The area of a rectangle (A) = length * width

A = x * (300 - x)

A = 300x - x²

The maximum area is at dA/dx = 0, hence:

dA/dx = 300 - 2x

300 - 2x = 0

2x = 300

x = 150 feet

y = 300 - x = 300 - 150 = 150 feet

The maximum area = x * y = 150 * 150 = 22500 feet²

The maximum area that can be enclosed is 22500 feet²

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