Question

a gardener has 440 feet of fencing to fence in a rectangular garden. one side of the garden is bordered by a river and so it does not need any fencing. What dimensions would guarantee that the garden has the greatest possible area?

Answer 1

Answer:

Dimensions would guarantee that the garden has the greatest possible area = 220 feet x 110 feet

Step-by-step explanation:

Fencing available = 440 feet

Here 3 sided need to be considered

That is

             Perimeter = 2x Length + width = 2l +w

             440 = 2l +w

              w = 440 - 2l

We have area = length x width

               A = lw

               A = l x (440 - 2l) = 440l - 2l²

For area to be maximum we have

               $\frac{dA}{dl}=0\\\\\frac{d}{dl}\left ( 440l - 2l^2\right )=0\\\\440-4l=0\\\\l=110feet$

Substituting in  w = 440 - 2l        

             w = 440 - 2 x 110 = 220 feet

Dimensions would guarantee that the garden has the greatest possible area = 220 feet x 110 feet