In a visual model, the large square is (16x^2) and the removed small square is (25). What will be the rectangle dimensions after rearrangement?

Correct answer: (4x+5) and (4x-5)

Direct answer: C. This is a difference-of-squares model. The large square has area 16x^2=(4x)^2, so its side is 4x. The removed square has area 25=5^2, so its side is 5. The remaining area is therefore (4x)^2-5^2. Using u^2-v^2=(u+v)(u-v), it rearranges into a rectangle with dimensions (4x+5) and (4x-5). Option A uses 25 itself as a side instead of taking its square root, so it confuses area with length. Option B uses 16x, the coefficient before squaring, rather than the side 4x. Option C correctly takes both square roots and applies the identity. Option D uses 2x, whose square is 4x^2, not 16x^2. A quick verification is to multiply C: (4x+5)(4x-5)=16x^2-25, exactly the remaining area.