A) The length of rectangle \( A \) is equal to the length of rectangle \( B \) only when \( x=1 \). B) The length of rectangle \( A \) is never equal to the length of rectangle \( B \). C) The length of rectangle \( A \) is always less than the length of rectangle \( B \). D) The length of rectangle \( A \) is always greater than the length of rectangle \( B \).

Did you know that rectangles have been used throughout history as one of the simplest geometric shapes for architectural designs? Ancient civilizations, like the Egyptians, utilized rectangles in their pyramids and temples, emphasizing their significance in various cultural contexts. Each rectangle’s dimensions can represent different ideals in design, with proportions believed to convey harmony and balance. If you're grappling with comparing lengths of rectangles in your math problems, a common mistake is not paying attention to the relationship between the variables involved. For instance, if the lengths depend on a variable like \( x \), remember to clarify how changes in \( x \) will affect each rectangle's length. Setting up a clear equation can often illuminate the comparison and the conditions under which one length is greater or equal to another!