Question

A gardener has 800 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.

garden bordered by a river

What dimensions would guarantee that the garden has the greatest possible area?

shorter side:
ft (feet)

longer side:
ft (feet)

greatest possible area:
ft2 (square-feet)

Answer 1

Explanation:

I'm assuming the sides can only be integers.

The most optimal area would be a square. We need to distribute 800 to 3 sides, which of course is not possible with integers. We will have to distribute the 800 as evenly as possible.

800/3 = 266.666666667.

We can let 2 sides be 267 and 1 side be 266. This will distribute it evenly. However, notices that the river side can be any length. Meaning that we can make one side be 268 and the other 2 sides be 266. This still satisfies our 800 feet of fencing, while being larger than 267 * 266.

Shorter side: 266 ft

Longer side: 268 ft

Greatest Possible Area: 71288