If, in a square model, the total area of the two middle rectangles is \(10x\) and the small square has area 25, what is the side of the complete square?

Correct answer: \(x+5\)

The direct answer is B: \(x+5\). The small square has area 25. Since the area of a square is side squared, its side is \(\sqrt{25}=5\). In the usual visual model for \(x^2+2cx+c^2\), the two middle rectangles have dimensions \(x\times c\) and \(x\times c\), so their combined area is \(2xc\). Here, \(2x\cdot5=10x\), confirming that the added length is 5. Therefore the complete square has side \(x+5\). A would make the two middle rectangles total \(20x\), not \(10x\). C represents a subtraction and would lead to a negative middle term. D confuses the area 25 with the side length; the side is the square root of the area, not the area itself. Memory cue: in a perfect-square area model, the small square gives the extra side length after taking its square root.