The perimeter of a rectangle is 12 in. If the length and width are whole numbers, what are the least and greatest possible areas?
3 by 3
1 by 5
To find the least and greatest possible areas of the rectangle, we need to consider all possible combinations of length and width that have a perimeter of 12 inches.
Let's start by listing all the possible combinations of length and width that have a sum of 6 inches (half the perimeter):
(1, 5)
(2, 4)
(3, 3)
(4, 2)
(5, 1)
Next, we can calculate the area of each combination by multiplying the length and width:
Area = Length * Width
For the first combination (1,5):
Area = 1 * 5 = 5 square inches
For the second combination (2,4):
Area = 2 * 4 = 8 square inches
For the third combination (3,3):
Area = 3 * 3 = 9 square inches
For the fourth combination (4,2):
Area = 4 * 2 = 8 square inches
For the fifth combination (5,1):
Area = 5 * 1 = 5 square inches
Therefore, the least possible area is 5 square inches (for combinations (1,5) and (5,1)), and the greatest possible area is 9 square inches (for the combination (3,3)).
So, the least possible area is 5 square inches, and the greatest possible area is 9 square inches.