a rectangle with a perimeter of 32 inches has whole-number side lengths. what is the difference between the greatest and the least areas of the rectangle?

49

Step-by-step explanation:

Let x represent the length and y represent the width of the given rectangle. The perimeter of the rectangle will be:

Perimeter = 2 (x + y)

32 = 2 (x + y)

16 = x + y

This means, the sum of length and width of the rectangle can be 16. Since only whole number side lengths are allowed, following are the possibilities:

Side Lengths: 15, 1 Area = 15 Side Lengths: 14, 2 Area = 28 Side Lengths: 13, 3 Area = 39 Side Lengths: 12, 4 Area = 48 Side Lengths: 11, 5 Area = 55 Side Lengths: 10, 6 Area = 60 Side Lengths: 9, 7 Area = 63 Side Lengths: 8, 8 Area = 64

Hence the largest possible value of Area is 64 and the least possible value is 15. The difference is 64 - 15 = 49