Afarmer has 260 feet of fencing to make a rectangular corral. what dimensions will make a corral with the maximum area? what is the maximum area possible?

Suppose we have a rectangle with a side of length L and another side of length (L-x). The area of the rectangle is

We impose the condition of maximum

Thus    

Hence the maximum area is when we have a square

With a perimeter  we obtain 
which gives A =L^2=65*65 =6225 ft^2

The least common multiple is 2. 2 is the highest number that goes in to each of these numbers.