Explanation:

- The sum of the length and width of rectangle R1 is 78 cm. Therefore, its perimeter is 2 × 78 = 156 cm.

- The sum of the length and width of rectangle R2 is 52 cm. Therefore, its perimeter is 2 × 52 = 104 cm.

- The difference in the perimeters of R1 and R2 is 156 - 104 = 52 cm.

- A square’s side is 1/4th of this difference: 52 / 4 = 13 cm.

- The area of this square is side × side = 13 × 13 = 169 square cm.

Therefore, the correct option is:

- Option 2: 169