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

Step-by-step explanation:

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