Answer:
Difference between the greatest and least possible areas of the rectangle = 20-8 = 12 inches.
Step-by-step explanation:
Let Length be denoted by L
and Breadth be denoted by B
then , Perimeter of rectangle is given by 2[tex]\times[/tex](L+B)
Given - Perimeter of rectangle be 18 inches.
2[tex]\times[/tex](L+B) = 18
L+B = 9
find the possible pairs of integers such that the sum of integers is 9
So, possible pairs arises are - 8,1 ; 7,2 ; 6,3 ; 5,4
Area of rectangle = Length [tex]\times[/tex] Breadth = L[tex]\times[/tex]B
finding area for each pair
8[tex]\times[/tex]1 = 8
7[tex]\times[/tex]2= 14
6[tex]\times[/tex]3= 18
5[tex]\times[/tex]4= 20
So , the greatest possible area is 20 inches and least possible area is 8 inches.
Thus, Difference between the greatest and least possible areas of the rectangle = 20-8 = 12 inches.