Asked by Ashlee
You want to build a garden around your garden. One side borders your house so it does not need a fence. If you only have 50m of fencing what dimensions should you make your garden in order to maximize the area?
Answers
Answered by
Reiny
Let the side parallel to the house by y
the each of the other two sides be x
Make a sketch
2x + y = 50
y = 50-2x
area = xy
= x(50-2x)
=50x - 2x^2
the x of the vertex of this parabola is -b/(2a) = -50/-4 = 12.5
so x = 12.5
and y = 50-25 = 25
The garden should be 25 m long and 12.5 m wide
by Calculus:
area = 50x - 2x^2
d(area)/dx = 50-4x = 0 for a max of area
4x=50
x = 12.5
continue as above
the each of the other two sides be x
Make a sketch
2x + y = 50
y = 50-2x
area = xy
= x(50-2x)
=50x - 2x^2
the x of the vertex of this parabola is -b/(2a) = -50/-4 = 12.5
so x = 12.5
and y = 50-25 = 25
The garden should be 25 m long and 12.5 m wide
by Calculus:
area = 50x - 2x^2
d(area)/dx = 50-4x = 0 for a max of area
4x=50
x = 12.5
continue as above
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