You have 32 feet of fencing and want to determine the maximum area that can be enclosed with the fencing to make a flower garden. You do not want to deal with fractions or decimals, so you are
limiting the dimensions to whole numbers. Also, the area is to be rectangular (or square) in shape.
Copy or print out the chart below to organize your work. (a) What are the dimensions of the figure
that yields the maximum area? (b) What is the area of the figure?

1- is the product of two rational numbers irrational or rational? first, make a hypothesis by multiplying two rational numbers. then, use variables such as x=a/b and y=c/d and the closure property of integers to prove your hypothesis. 2- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis. 3- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in part b?