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A farmer has 500 feet of fence for constructing a rectangular corral. One side of the corral will be formed by the barn and requires no fence. Three exterior fences and two interior fences partition the corral into three rectangular pens. What are the dimensions of the corral that maximize the enclosed area? What is the area of the three pens?

Respuesta :

ishadevbarman

Answer:

no there none answer .......

mathstudent55

Answer:

The corral is 250 ft by 62.5 ft.

The area of each pen is 5208.3 ft².

Step-by-step explanation:

Let x = length along barn.

Let y = width, and also length of the partitions.

x + 4y = 500

x = 500 - 4y

A = xy

A = (500 - 4y)y

A = 500y - 4y²

dA/dy = 500 - 8y

500 - 8y = 0

8y = 500

y = 62.5

x = 500 - 4y

x = 500 - 4(62.5)

x = 500 - 250

x = 250

The corral is 250 ft by 62.5 ft.

Area of each pen:

x/3 × y = 250 ft / 3 × 62.5 ft =

= 5208.3 ft²

The area of each pen is 5208.3 ft²

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