SOLUTION: Mike wants to enclose a rectangular area alongside his barn using 30 feet of fencing. What dimensions will maximize the area fenced in if the barn is used for one side of the r ect

Question 813326: Mike wants to enclose a rectangular area alongside his barn using 30 feet of fencing. What dimensions will maximize the area fenced in if the barn is used for one side of the r ectangle?
Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
L + 2w = 30
L = 30 - 2w
A = Lw
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A = (30 - 2w)w
A = 30w - 2ww
A(w) = -2ww + 30w + 0
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the above quadratic equation is in standard form, with a=-2, b=30, and c=0
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to solve the quadratic equation, plug this:
-2 30 0
into this: https://sooeet.com/math/quadratic-equation-solver.php
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Answer 1:
the vertex of the quadratic equation is a maximum point at: ( w=7.5, A(w)=112.5 )
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w = 7.5 feet
L = 30 - 2w
L = 30 - 2(7.5) = 15 feet
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Answer 2:
the max area is: 112.5 sq.ft.
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