Why is 28 square units not a possible area for a rectangle with a width of 3 units?

$$\text{Area} = \text{length} \times \text{width}$$

We are given that the area is 28 square units and the width is 3 units.

$$28 = \text{length} \times 3$$

To find the length, divide the area by the width:

$$\text{length} = \frac{28}{3}$$ $$\text{length} = 9\frac{1}{3} \text{ units}$$

The length of the rectangle would be $9\frac{1}{3}$ units. In many elementary contexts, when discussing areas in "square units," it is implied that the side lengths are whole numbers. Since $9\frac{1}{3}$ is not a whole number, it means that a rectangle with a width of 3 units cannot have an area of exactly 28 square units if we are restricted to whole number lengths.

The area of 28 square units is not possible for a rectangle with a width of 3 units because the required length, $\frac{28}{3}$ units, is not a whole number.