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A farmer has 324 feet of fencing to make three identical adjacent rectangular pens, as shown in the picture. What dimensions of each pen will maximize the total enclosed area?

A Farmer Has 324 Feet Of Fencing To Make Three Identical Adjacent Rectangular Pens As Shown In The Picture What Dimensions Of Each Pen Will Maximize The Total E class=

Sagot :

abiolataiwo2015

The dimensions of each pen will maximize the total enclosed area are:  Length 81 feet; Width 81 feet.

Dimension of each pen

Length = x

Width = y

Area = xy

Perimeter equation is

2(x + y) = 324

  x + y = 162

Substituting the perimeter equation

Area = x(162 - x)

Area = -x2 + 162x

If the zeros of the quadratic are 0 and 162, then the median  will be where the maximum area occurs.

162/ 2

= 81

Hence, the dimensions are

Length = 81 feet

Width = 162 - 81 = 81 feet

Therefore the dimensions of each pen will maximize the total enclosed area are:  Length 81 feet; Width 81 feet.

Learn more about dimension here:https://brainly.com/question/26740257

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