What is the largest possible area (in square inches) for a rectangle with a perimeter of 120 inches

Answer 1

That would be a square with sides of 30 in.

Answer 2

Let's create a table of possibilities. We can start with a length of 10. If the perimeter is 120 then the width must be 50 (because 10 + 10 + 50 + 50 = 120). Then pick a length of 15 and calculate the corresponding width of 45 (because 15 + 15 + 45 + 45 = 120). Here is the table:

Notice that the largest area is 900 square inches (when the rectangle is actually a square).