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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?

User Drescherjm
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1 Answer

4 votes

Answer:

49

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

User Vadim Yangunaev
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