On a centimeter dot array, draw all possible rectangles with a perimeter of 12 cm and sides whose lengths are whole centimeters. Label the lengths of two adjacent sides of each rectangle.

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P = 2L + 2W

1 by 5
2 by 4
3 by 3

1 by 5

2 by 4
3 by 3

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Oh, joy! It's time for some geometric fun! Let's get down to it, shall we?

Here are all the possible rectangles that have a perimeter of 12 cm on a centimeter dot array:

Rectangle 1:
Sides: 1 cm x 5 cm

Rectangle 2:
Sides: 2 cm x 4 cm

Rectangle 3:
Sides: 3 cm x 3 cm

And that's it! We've covered all the possible rectangles that fit the criteria. Now, go ahead and try drawing them on your centimeter dot array. Enjoy the puzzling shapes!

To solve this problem, we need to find all the possible rectangles on a centimeter dot array, with a perimeter of 12 cm and whole number side lengths.

First, let's consider the possible rectangle dimensions by listing all possible pairs of factors of 12.

Factor pairs of 12 are: (1, 12), (2, 6), and (3, 4).

Now, we can use these factor pairs to draw the rectangles on the centimeter dot array.

For the factor pair (1, 12), it means one side of the rectangle is 1 cm and the other side is 12 cm. On the centimeter dot array, you can draw a rectangle by creating a row of dots for the shorter side and a column of dots for the longer side. Label these dimensions on the sides of the rectangle.

For the factor pair (2, 6), one side of the rectangle is 2 cm and the other side is 6 cm. Repeat the same process on the centimeter dot array by creating a row of dots for the shorter side and a column of dots for the longer side. Label these dimensions.

Finally, for the factor pair (3, 4), one side of the rectangle is 3 cm and the other side is 4 cm. Draw the rectangle on the centimeter dot array using the same method as before. Label the dimensions once again.

After drawing all the rectangles using the three factor pairs, you would have all the rectangles on the centimeter dot array with a perimeter of 12 cm and whole number side lengths.