The difference between the greatest and least areas is 72 square inches.
What is perimeter of a rectangle?
Let L be the length and w be the width of the rectangle.
Perimeter = 2l + 2w = 48
Since each side is a whole number, list pairs of whole numbers that satisfy the equation.
Potential pairs (length, width) are:
(23, 1)
(22, 2)
(21, 3)
(20, 4)
(19, 5)
Let's calculate the areas for the pairs mentioned:
Area = l*w
(23, 1)) A = 23* 1 = 23
(22, 2) A = 22 *2 = 44
(21, 3) A = 21 *3 = 63
(20, 4) A = 20 *4 = 80
(19, 5) A = 19 *5 = 95
The greatest area is 95 square inches, and the least area is 23 square inches.
The difference between the greatest and least areas is 95 - 23 = 72 square inches. Therefore, the answer is 72.