A square of side a + b is cut into four parts and rearranged into a rectangle. If one side of the rectangle remains a + b, what is the other side?

Correct answer: a + b

The direct answer is B: the other side is a + b. The original square has side a + b, so its area is (a + b)². Cutting and rearranging the pieces does not change the total area. The new rectangle has one side a + b, so let its other side be L. Its area is (a + b)L. Because the area is unchanged, (a + b)L = (a + b)². For a valid positive side length, divide by a + b to obtain L = a + b. A, a − b, would generally produce a different area and may not even be positive for all values. C, 2a + 2b, would make the rectangle twice as large when multiplied by the unchanged side. D, ab, has the wrong form and does not preserve the original area. The key idea is conservation of area: rearrangement changes shape, not total area. Memory cue: same area plus one same side forces the other side to remain the same.