Draw all the possible rectangles with a perimeter of 26 cm and whole number lengths of sides. For each rectangle, label the lengths of two adjacent sides

P = 2L + 2W

1 by 12
2 by 11
3 by 10

Take it from there.

To find all the possible rectangles with a perimeter of 26 cm and whole number lengths of sides, we need to consider the factors of 26.

The factors of 26 are: 1, 2, 13, and 26.

Now, let's list down all the possible combinations of these factors that could represent the lengths of two adjacent sides of a rectangle:

For a length of 1:
- The other length would be 26 - 1 = 25. So, one possible rectangle is a 1 cm by 25 cm rectangle.

For a length of 2:
- The other length would be 26 - 2 = 24. So, one possible rectangle is a 2 cm by 24 cm rectangle.

For a length of 13:
- The other length would be 26 - 13 = 13. So, one possible rectangle is a 13 cm by 13 cm square.

For a length of 26:
- The other length would be 26 - 26 = 0, which is not a valid length for a rectangle.

Therefore, the possible rectangles with a perimeter of 26 cm and whole number lengths of sides are:
1 cm by 25 cm (lengths of two adjacent sides are 1 cm and 25 cm)
2 cm by 24 cm (lengths of two adjacent sides are 2 cm and 24 cm)
13 cm by 13 cm (lengths of two adjacent sides are 13 cm and 13 cm, forming a square)