Question

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?

Answer 1

The difference is 12

first we should find out how much is the sum of length and width :
$18 \div2 = 9$
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
$1 \times 8 = 8$

now let's find 2 numbers with sum of 9 and greatest possible area.
they are 4 and 5. the area is:
$4 \times 5 = 20$

the final answer will be the difference between these two areas
$20 - 8 = 12$

good luck