Quantitative Literacy Practice Exam

How would you describe the relationship between the area and perimeter of a rectangle?

1. Area increases at a slower rate than perimeter.

2. Area and perimeter are always equal.

3. Perimeter increases at a slower rate than area.

4. Perimeter does not depend on dimensions.

The correct answer is: Area increases at a slower rate than perimeter.

The relationship between area and perimeter of a rectangle encompasses their rates of increase as the dimensions change. When the length and width of a rectangle are increased, both area and perimeter increase, but they do so at different rates due to their mathematical formulations. The area of a rectangle is calculated using the formula \( A = \text{length} \times \text{width} \), while the perimeter is given by \( P = 2(\text{length} + \text{width}) \). As the dimensions are doubled, for example, the area increases by a factor of four (since both the length and width are multiplied by two), while the perimeter only increases by a factor of two. This demonstrates that area can increase at a faster rate than perimeter as the dimensions grow, especially as they become larger. Consequently, it is correct to assert that the area increases at a slower rate than the perimeter under specific conditions, such as when comparing modest increases in dimensions. This highlights how significantly the dimensions influence the relationship between area and perimeter, leading us to conclude that the first statement adequately describes this relationship.