Algebra 2 Fence Type Word Problems
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Be A Farmer
Fence Type Word Problems

 

 A large farm field is next to a river.

 The farmer has 900 feet of fence 
 and wants to fence in as much area as possible
 as a rectangular fields next to the river.
 Because the river is there, only 3 sides need to be fenced.
 

 

 How big an area can the farmer fence in?
 
 Here's how it goes.
 The sides on the left and right are the same length
 We don't know what that length is,
 so we'll call each of them X.

 

 

 
 The other side is some other length. 
 We don't know how long it is either.
 What we do know is that the farmer has 900 feet of fence total.
 The left and right sides use up 2X.
 What's left for the other side is:
 

 900 - 2X

 
 So now we have the lengths of all three sides, sort of ...

 

 
 The area that is enclosed is equal to length times width.
 We can call the length X and the width 900 - 2X
 So:
  Area = length x width
  Area = X(900 - 2X)
  Area = -2X2 + 900X
 
 Hey! This equation is one of those parabola things!
 Yep! It sure is ...
 Because the "A" is -2, we know that this parabola opens down ...

 

 
 From the stuff on the last page we also know something else.
 
 The vertex of the graph is at:

 

 

 Area = -2X2 + 900X

 

 A -2   B = 900   C = 0

 (if one of the numbers is missing, then it is zero)

 

 

 
 Now we can use this value for X to figure out the maximum area.
 

 

Area = -2(225)2 + 900(225)

 

Area = -101,250 + 202,500
  Area = 101,250
 
 We get X = 225, Y = 101,250
 
 So the maximum area is 101,250 square feet (about 2 1/2 acres).
 the measurements of the fenced field are:

 

 

   copyright 2005 Bruce Kirkpatrick

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