A rectangular rug has a base b and a height h, with a perimeter of 30 feet. Both b and h are both whole numbers between 5 and 10 feet. Fill in the blanks to complete this sentence:
The area of the rug is at least _______ but not greater than ______.
The dimensions must be:
5 by 10
6 by 9
7 by 8
A = LW
Multiply the dimensions to find the possible areas.
To find the range of possible areas for the rectangular rug, we need to consider the perimeter of the rug and the given constraints for the base and height.
First, let's analyze the formula for the perimeter of a rectangle:
Perimeter = 2 * (base + height)
Given that the perimeter is 30 feet, we can write the equation as:
30 = 2 * (b + h)
Now, let's substitute the possible whole number values for b and h (between 5 and 10) into the equation to find the minimum and maximum values for the area.
For the minimum possible area, we need to consider the smallest possible values for b and h within the given range. Let's assume b = 5 and h = 5:
30 = 2 * (5 + 5)
30 = 2 * 10
The perimeter is 30 feet, so the minimum possible area is 5 * 5 = 25 square feet.
For the maximum possible area, we need to consider the largest possible values for b and h within the given range. Let's assume b = 10 and h = 10:
30 = 2 * (10 + 10)
30 = 2 * 20
The perimeter is 30 feet, so the maximum possible area is 10 * 10 = 100 square feet.
Therefore, completing the sentence, we can say:
"The area of the rug is at least 25 square feet but not greater than 100 square feet."