If Mr. Sanchez has 16 feet of fencing to put around a rectangular garden.he wants the garden to have the greatest possible area. How long should the sides of the garden be?
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let x=width of garden
let y=length of garden
2x+2y=perimeter=16
2y=16-2x
y=8-x
area=x*y=x(8-x)=8x-x^2
area=-x^2+8x
complete the square:
A(x)=-(x^2-8x+16)+16
A(x)=-(x-4)^2+16
this is an equation of a parabola that opens down with vertex at (4,16)
maximum area of the garden of 16 sq ft occurs when:
width=4 ft
length=4 ft
a square
