Answer:
Difference between the greatest and least possible areas of the rectangle = 20-8 = <u>12 inches.</u>
Step-by-step explanation:
Let Length be denoted by L
and Breadth be denoted by B
then , Perimeter of rectangle is given by 2(L+B)
Given - Perimeter of rectangle be 18 inches.
2(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 Breadth = LB
finding area for each pair
81 = 8
72= 14
63= 18
54= 20
So , the greatest possible area is 20 inches and least possible area is 8 inches.
<u>Thus, Difference between the greatest and least possible areas of the rectangle = 20-8 = 12 inches.</u>