Dania has laid out floor tiles so they form a rectangle with a perimeter of 18 inches. what is the difference between the greatest and least possible area of the rectangle?

The difference is 12

first we should find out how much is the sum of length and width :

so we have to find 2 numbers with sum of 9
and least possible area.
the numbers will be 1,8 and the area is


now let's find 2 numbers with sum of 9 and greatest possible area.
they are 4 and 5. the area is:


the final answer will be the difference between these two areas


good luck