Question

A gardener has 120 ft 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.

a. what dimensions would guarantee a garden with an area of 1350 ft ^2
b. what dimensions would guarantee the greatest area? how much is the greatest area?

Answer 1

If the dimensions are x and y,

2x+y=120
xy = 1350

Solve that to get x and y. There are two possible solutions.

Note that the area is

xy = x(120-2x) = 120x-2x^2

That's just a parabola. The vertex represents the maximum area.