The width of the rectangle, equal to 12 cm, is 1/5 of the rectangle’s perimeter.

The width of the rectangle, equal to 12 cm, is 1/5 of the rectangle’s perimeter. Find the area of a square whose perimeter is equal to the perimeter of this rectangle.

Obviously, if the width of a rectangle is 12 cm and it is one fifth of its perimeter, then the perimeter of this rectangle is 5 times its width. Therefore, the perimeter of the rectangle is 5 * (12 cm) = (5 * 12) cm = 60 cm.
According to the condition of the assignment, the perimeter of the square is equal to the perimeter of this rectangle, that is, the perimeter of the square is 60 cm.Since the square has 4 equal sides, its side is (60 cm): 4 = (60: 4) cm = 15 cm.
Therefore, the area of the square is (15 cm) ² = 15² cm² = 225 cm².
Answer: 225 cm².