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Maximizing Area

A farmer has 200 ft of fencing and wants to build three adjacent rectangular corrals. Determine the dimensions that should be used to maximize the area, and find the area of each individual corral.
 
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Mark M. | Mathematics Teacher - NCLB Highly QualifiedMathematics Teacher - NCLB Highly Qualif...
5.0 5.0 (141 lesson ratings) (141)
1
200 - 2y = 4x
100 - y = 2x        divide both sides by 2
100 = 2x + y       add y to both sides
100 - 2x = y        subtract 2x from both sides
 
A = x(100 - 2x)
A = 100x - 2x2
A = -2x2 + 100x
 
Maximum is at x = -100/2(-2)       maximum at -b/2a
Maximum at x = 25
y = 50
 
What is the area of each pen?