Asked by sarah
A rectangular dog pen is constructed using a barn wall as one side and 50 meters of fencing for the other three sides. What is the maximum area of the dog pen?
Answers
Answered by
mathhelper
length of side parallel to barn === y
length of each of other two sides === x
so we have 2x + y = 50
y = 50-2x
area = xy = x(50-2x)
= -2x^2 + 50x
We need the vertex of this parabola
the x of the vertex = -50/-4 = 12.5
then y = 50-2(12.5) = 25
so max area = xy = 12.5(25) m^2 or 312.5 m^2
You could also find x by completing the square,
or by Calculus setting the derivative of -2x^2 + 50x equal to zero
length of each of other two sides === x
so we have 2x + y = 50
y = 50-2x
area = xy = x(50-2x)
= -2x^2 + 50x
We need the vertex of this parabola
the x of the vertex = -50/-4 = 12.5
then y = 50-2(12.5) = 25
so max area = xy = 12.5(25) m^2 or 312.5 m^2
You could also find x by completing the square,
or by Calculus setting the derivative of -2x^2 + 50x equal to zero
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