Question

Which real-world problem is most likely to involve irrational numbers?(1 point)
Responses

finding the width of a rectangle based on the area and the length
finding the width of a rectangle based on the area and the length

finding the diameter of a circle based on the radius
finding the diameter of a circle based on the radius

finding the side length of a square based on the area
finding the side length of a square based on the area

finding the total cost of filling up a car’s tank based on the price per gallon

Answer 1

Finding the width of a rectangle based on the area and the length is most likely to involve irrational numbers. This is because, when calculating the width, you would use the formula \( \text{width} = \frac{\text{area}}{\text{length}} \). If the area does not result in a rational division when using a length that does not factor into the area perfectly, this could lead to an irrational number as a solution.

Similarly, finding the side length of a square based on the area also involves square roots, which can produce irrational numbers, particularly when the area is not a perfect square.

However, the one response that typically results in an irrational number is finding the side length of a square based on the area, since the side length of a square is found by taking the square root of the area.

In general:
- The square root of a non-perfect square yields an irrational number.

To summarize, while both the width of a rectangle and side length of a square may involve irrational numbers, finding the side length of a square based on the area more commonly leads to an irrational number due to the square root operation.