On a centimeter dot array, draw all possible rectangles with a perimeter of 16cm and sides whose lengths are whole centimeters. Label the lengths of two adjacent sides of each. Also the area of each rectangle. Compare the shapes of the rectangles with the least and greatest areas.

greatest area: 4x4

least area: 1x7

16

Rectangles of Two adjacent sides

To draw all possible rectangles with a perimeter of 16cm on a centimeter dot array, we can start by considering the possible combinations of side lengths that add up to a perimeter of 16cm. Since the problem specifies whole centimeters, we need to find pairs of numbers that add up to 8.

Here are the possible combinations:

1) Length of one side: 1cm, Length of adjacent side: 7cm (1 + 7 = 8)
Area: 1cm * 7cm = 7cm²

2) Length of one side: 2cm, Length of adjacent side: 6cm (2 + 6 = 8)
Area: 2cm * 6cm = 12cm²

3) Length of one side: 3cm, Length of adjacent side: 5cm (3 + 5 = 8)
Area: 3cm * 5cm = 15cm²

4) Length of one side: 4cm, Length of adjacent side: 4cm (4 + 4 = 8)
Area: 4cm * 4cm = 16cm²

Now let's compare the shapes of the rectangles with the least and greatest areas.

The rectangle with the least area has dimensions of 1cm by 7cm and an area of 7cm². This rectangle would be a long and narrow shape.

The rectangle with the greatest area has dimensions of 4cm by 4cm and an area of 16cm². This rectangle would be a square shape.

Therefore, the rectangle with the least area is long and narrow, while the rectangle with the greatest area is a square.