Question

A Gardener has 560 feet of fencing to fence in a rectangular garden. One side of the garden is bordered by a river so it does not need any fencing. What dimensions would guarantee that The Gardener has the greatest possible area

Answer 1

The dimensions that give the largest possible area are 186 by 187, with an area of 34,782ft².

To maximize area and minimize perimeter, you make the figure as close to equilateral as possible. 560/3 = 186 2/3. We would rather use whole number dimensions, so we would have 186 for one side. 560-186 = 374. 374/2 = 187 for the other dimension.

Answer 2

Each side of the garden should be 186.67 feet

Explanation:

We know that the biggest area of a rectangular prism is when it closer to a square, and we know that a square is a special kind of rectangle with all equal sides, so we want all the sides to be equal.

To do this we know that the Gardener has 560 feet of fencing and he is only going to fence 3 sides because the other side is bordered by a river.

So we have to divide the fencing by the sides to have equal sides:

560 feet / 3 sides = 186.67 feet per side.

So the garden will be a square with each side of 186.67 feet, and the area will be:

186.67 * 186.67 = 34,845.70 square feet.