Final answer:
To determine the side length of a square with an area of 18 square feet, one must take the square root of the area. The square root of 18 is approximately 4.2426 feet, which rounds to the nearest option of 4.5 feet, thus the length of the window's side is 4.5 feet.
Step-by-step explanation:
The task of determining the length of one side of a square window, given its area as 18 square feet, involves the application of fundamental geometric principles. The formula for the area of a square is expressed as \( \text{area} = \text{side length}^2 \). To find the side length, one can reverse this process by taking the square root of the area: \( \text{side length} = \sqrt{\text{area}} \).
In this specific case, where the area of the square window is given as 18 square feet, the calculation involves taking the square root of 18. The result is approximately 4.2426 feet. However, since the provided options are discrete values, the closest option is chosen. Rounding to the nearest available option yields 4.5 feet, which corresponds to option b).
This process not only solves the immediate problem at hand but also illustrates the broader application of mathematical concepts in real-world problem-solving. Understanding the relationship between the area and side length of a square is fundamental to various fields, including architecture, engineering, and design. The ability to manipulate and interpret geometric formulas is a valuable skill, allowing individuals to make practical decisions and calculations based on quantitative information. In this case, it enables the determination of the side length of the square window, facilitating tasks such as construction or fitting within a given space.