Math
posted 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?

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 = 502x
area = xy
= x(502x)
=50x  2x^2
the x of the vertex of this parabola is b/(2a) = 50/4 = 12.5
so x = 12.5
and y = 5025 = 25
The garden should be 25 m long and 12.5 m wide
by Calculus:
area = 50x  2x^2
d(area)/dx = 504x = 0 for a max of area
4x=50
x = 12.5
continue as above
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