What is the perimeter of a rectangle if each side is a whole number of meters,and what are the possible dimensions for the length and width. List them and explain your answer.
2w+2L
any old whole numbers for L and w
To find the perimeter of a rectangle, you need to add together all four sides. Since each side is a whole number of meters, we can assume that the length and width are positive integers.
Let's represent the length of the rectangle as "L" and the width as "W".
The formula for finding the perimeter of a rectangle is:
Perimeter = 2L + 2W
Now, let's list possible dimensions of the length and width. Since both the length and width should be positive integers, we can list different combinations that satisfy this condition.
1. If we let L = 1 meter and W = 1 meter, the perimeter would be: 2(1) + 2(1) = 2 + 2 = 4 meters.
2. If we let L = 2 meters and W = 1 meter, the perimeter would be: 2(2) + 2(1) = 4 + 2 = 6 meters.
3. If we let L = 1 meter and W = 2 meters, the perimeter would be: 2(1) + 2(2) = 2 + 4 = 6 meters.
4. If we let L = 2 meters and W = 2 meters, the perimeter would be: 2(2) + 2(2) = 4 + 4 = 8 meters.
5. If we let L = 3 meters and W = 1 meter, the perimeter would be: 2(3) + 2(1) = 6 + 2 = 8 meters.
6. If we let L = 1 meter and W = 3 meters, the perimeter would be: 2(1) + 2(3) = 2 + 6 = 8 meters.
These are some possible dimensions and their corresponding perimeters. However, there are infinitely many possibilities since the length and width can continue to increase while being positive integers.