Question

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?

Answer 1

Answer:

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