application: farmer has 200 m of fencing for rect. field

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mazibeth

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Kindly assist with this problem:

--A farmer has 200 meters of fencing with which to enclose a rectangular field. One side of the field can make use of a fence that already exists. What is the maximum area that can be enclosed?
 
Re: application of equatios and functions

mazibeth said:
Kindly assist with this problem:

--A farmer has 200 meters of fencing with which to enclose a rectangular field. One side of the field can make use of a fence that already exists. What is the maximum area that can be enclosed?
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To begin Name variables:

A(rea) = L(ength) * W(idth)

For rectangular area (without one side)

P(erimeter) = 200 = L + 2*W

Now continue....

Please show us your work and exactly where you are stuck - so that we know where to begin to assist you.
 
This is a problem that is in most algebra books, in one form or another.

After writing an equation for the area of the field, you substitute for one of the variables, and get a quadratic equation in a single variable. The maximum area is found at the vertex of the parabola, which can be found by using the formula x = -b/(2a).
 
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