The area of a square is equal to the area of a rectangle with sides of 60 mm. and 24 cm.

The area of a square is equal to the area of a rectangle with sides of 60 mm. and 24 cm. What is the side of an equilateral triangle whose perimeter is half the perimeter of the square.

Since 60 mm = 6 cm, the area of this rectangle is
S = 6 * 24 = 144 cm².
Thus, if the area of the square is equal to the area of the rectangle, then the side of the square is:
a² = 144,
a = √144,
a = 12 (cm).
This means that the perimeter of this square is:
P = 4 * 12 = 48 (cm).
Since the perimeter of an equilateral triangle is P = 3 * a, where a is the side length of this triangle, and by the condition of the problem is half the perimeter of the square, we get:
3 * a = 24,
a = 24: 3,
a = 8 (cm).
Answer: 8 cm.