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