Question

which real-world problem is most likely to involve irrational numbers? (1 point)
○ finding the total cost of filling up a car’s tank based on the price per gallon
○ finding the diameter of a circle based on the radius
○ finding the side length of a square based on the area
○ finding the width of a rectangle based on the area and the length

Explanation:

1. Analyze each option:

• For "finding the total cost of filling up a car’s tank based on the price per gallon", the cost is usually a rational number (price per gallon times gallons, both likely rational).
• For "finding the diameter of a circle based on the radius", the formula is \(d = 2r\). If \(r\) is rational, \(d\) is rational.
• For "finding the side length of a square based on the area", the formula is \(s=\sqrt{A}\). If the area \(A\) is a non - perfect square (e.g., \(A = 2\)), then \(s=\sqrt{2}\), which is an irrational number.
• For "finding the width of a rectangle based on the area and the length", the formula is \(w=\frac{A}{l}\). If \(A\) and \(l\) are rational, \(w\) is rational.

Answer:

finding the side length of a square based on the area