Use calculus to find the largest possible area for a rectangular field that can be enclosed with a fence that is 500 meters long.

The maximum area that can be enclosed is 15625 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)

500 = 2(x + y)

250 = x + y

y = 250 - x

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

A = x * (250 - x)

A = 250x - x²

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

dA/dx = 250 - 2x

250 - 2x = 0

2x = 250

x = 125 feet

y = 250 - x = 250 - 125 = 125 feet

The maximum area = x * y = 125 * 125 = 15625 feet²

The maximum area that can be enclosed is 15625 feet²

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step-by-step explanation:

we are given

since, we have to isolate x on anyone side

so, we can move all x terms on one side

subtract both sides by 2x

add both sides by 9

divide both sides by 4

we get

the answer is 1/4

step-by-step explanation: