SOLUTION: A rectangular pen is to be built against a wall using 60 m of fencing for the three sides which need fencing. If the area of the pen is to be as large as possible, find the length

Question 937287: A rectangular pen is to be built against a wall using 60 m of fencing for the three sides which need fencing. If the area of the pen is to be as large as possible, find the length of the longest side and also its maximum area.
Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
a = xy
y + 2x = 60
y = 60 - 2x
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a = x(60 - 2x)
a = 60x - 2xx
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-2xx + 60x = 0
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the above quadratic equation is in standard form, with a=-2, b=60 and c=0
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to solve the quadratic equation, by using the quadratic formula, copy and paste this:
-2 60 0
into this solver: https://sooeet.com/math/quadratic-equation-solver.php
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the quadratic has two real roots at:
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x = 0
x = 30
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the quadratic has a vertex maximum at: ( 15, 450 )
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maximum area (a) occurs when x = 15:
y = 60 - 2*15
y = 30 m
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answer:
x = 15 m
y = 30 m
max area = 450 sq.m
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