Is the length of a rectangle a function of its area?

Question

Area of a
rectangle (cm
2
) Length of a
rectangle (cm)
16 8
16 4
16 16

The length of a rectangle is
of its area because for every input there is
possible output.

Answer 1

The length of a rectangle is not a function of its area. This is because for a given area, there can be multiple possible lengths corresponding to different widths.

In the examples you provided, the area of the rectangle is 16 cm². The lengths you listed (8 cm, 4 cm, and 16 cm) correspond to different widths (2 cm, 4 cm, and 1 cm, respectively), which all result in the same area.

For example:

• If the length is 8 cm, the width must be 2 cm (since \(8 \times 2 = 16\)).
• If the length is 4 cm, the width must be 4 cm (since \(4 \times 4 = 16\)).
• If the length is 16 cm, the width must be 1 cm (since \(16 \times 1 = 16\)).

Therefore, since for the same area (16 cm²) there are multiple lengths possible, we conclude that the length of a rectangle is not a function of its area because, for every input (the area), there are multiple possible outputs (lengths).