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

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Mathematics

Kenneth Cannon

5 March, 00:17

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

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Gould · 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.