a gardener wishes to fence the perimeter of a rectangular garden with an area of 120 square feet. if the garden is x feet long, express the amount L of fence needed as a function of x
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Answer:
We call x to width and y to high
If perimeter is 120, then
2x+2y=120 , or y=60−x
The surface
s(x)=x⋅y=x(60-x)is the surface area as function of width
If we want to maximize area, then s(x)=60−2
x=0 and we obtain as solution
x=30and then the surface will be maximum if rectangle is a square with 30 ft of side