Question 3405
As per question x represent the length of the side of the rectangle
along the river. Let the width of garden be y.

The length of fence = x + 2y = 80

and the area of the garden = xy

We need to maximize the area of the garden.

Suppose x = 40+k where k is some constant either positive or negative

The equation for fencs is
{{{x + 2y = 80}}}

On putting x = 40+k in the above equation:
{{{(40+k) + 2y = 80}}}
{{{2y = 80-40-k}}}
{{{y = 20-k/2}}}

The area of garden is xy.

On putting the value of x and y in terms of k in area:
{{{Area = (40+k)*(20-k/2)}}}
{{{Area = 800-k^2/2}}}

To maximize the area, we need to take the value of k = 0.

Then, Area = 800 square meter

and x = 40 and y = 20.