Final answer:
The question appears to be incomplete and lacks sufficient information to find the value of x for congruent sides of a rectangle. For a different scenario involving squares, if the side length doubles, the larger square will have four times the area of the smaller one.
Step-by-step explanation:
The student's question involves finding the value of x when two sides of a rectangle are congruent and are represented by algebraic expressions. Since rectangles have congruent opposite sides, if one side is represented by 2x and the other side by 3x, 4x, or 5x, we know that these expressions must be equal to each other for the sides to be congruent.
However, without additional information such as a specific algebraic equation or details about the dimensions of the rectangle, it's not possible to determine which expressions represent the congruent sides or to solve for x. The problem as shared appears to be missing information that is critical to solving for x.
In a different problem, if we know the sides of a square and we are comparing it to a larger square with sides twice as long, then we can compute the area of the larger square. For instance, if Marta has a square with a side length of 4 inches, and she has a similar square that is twice as large, the side length of the larger square would be 4 inches x 2 = 8 inches. The area of this larger square would thus be 8 inches x 8 inches = 64 square inches, which is four times the area of the smaller square (since area scales with the square of the side lengths).