# Math

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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?

• Math -

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

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