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A farmer builds a fenced-in, rectangular pen for goats to clear brush from a section of land. The
pen has three sides of fencing because the width of the pen sits against the side of a barn.
If the farmer has 180 feet of fencing, what dimensions maximize the area of the pen?

a. 40 ft by 100 ft
b. 45 ft by 45 ft
c. 45 ft by 90 ft
d. 50 ft by 65ft

Respuesta :

The dimension that maximize the are of the pen is 45 ft by 90 ft.

Area of a rectangle

  • area = lw

where

l = length

w= width

Therefore,

perimeter of a rectangle = 2(l + w)

The barn is occupying one part of the rectangle . Therefore,

perimeter = 2l + w

180 = 2l + w

w  = 180 - 2l

area = lw

Therefore,

area = l(180 - 2l)

area = 180l - 2l²

To maximize area

l = -b / 2a

l = - (180) / 2 × -2

l = -180 / -4

l = 45 ft

Therefore,

w = 180 - 2(45)

w = 180 - 90

w = 90 ft

learn more on rectangle here:  https://brainly.com/question/12685460

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