On the Fence
Allen wants to build a fence in his backyard for his herb garden out of the 14 feet of fencing he owns wants to fence off as small an area as possible to leave room for his other plants. Using all of the fencing, what is the smallest possible area he can fence off in square feet?
The answer is 6.
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1 solution
First of all, you have to mention that all side lengths are positive integers. But after that, you see that any two adjacent side lengths must add up to 7 (to have a total perimeter of 14). To minimize the area, we see that 1 and 6 work, and their product is 6.