Hernan M.

asked • 02/12/17

two hundred feet of fencing is used to fence in a backyard with three separate sections. What is the largest possible area that can be enclosed?

The fencing will be done next to a house, so there wont be any fencing along the side of the house

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Mark M. answered • 02/12/17

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Draw and label a diagram.
One section of fence parallel to the house.
Four sections of fence perpendicular to the house.
w represents the length of each perpendicular
200 - 4w represents the length of the parallel fence
 
A = w(200 - 4w)
A = 200w - 4w2
 
Can you determine the maximum (it is at the vertex)?
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Hernan M.

I would have to complete the square to find the vertex right?
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02/12/17

Mark M.

That is one option. Another is that the vertex is at w = -b/2a. In this case that is w = -200/2(-4).
What is the value of w?
What is the area of the rectangle?
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02/12/17

Hernan M.

w=25
 A=200(25)-4(25)^2
5000-2500=2500?
 
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02/12/17

Hernan M.

w=25
A=200(25)-4(25)^2
5000-2500= 2500?
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02/12/17

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