The square's circumference depends on how it's divided. In common scenarios, it can be either 8/3 (approx. 2.67) if diagonals form triangles, or 4√(4/15) (approx. 1.53) if connecting midpoints creates triangles. Without specific division method, a precise answer is impossible.
The answer depends on the specific way the square is divided into 4 triangles. There are multiple possibilities, each leading to a different square circumference. Here are two common scenarios:
Scenario 1: Diagonals divide the square into right triangles:
Imagine diagonals intersecting in the center of the square, creating four right triangles.
Since each triangle has three sides of equal length, the total circumference of each triangle is 3 times the side length.
We know the triangle circumference is 1, so the side length of each triangle is 1/3.
The square's side length is twice the diagonal length in a right triangle. Therefore, the square's side length is 2 * (1/3) = 2/3.
Finally, the square's circumference is 4 times its side length, which is 4 * (2/3) = 8/3.
Therefore, in Scenario 1, the square's circumference is 8/3, approximately 2.67.
Scenario 2: Triangles formed by connecting midpoints of opposite sides:
Divide the square by connecting the midpoints of opposite sides, creating four isosceles triangles.
Each triangle has two sides equal to half the square's side length and a base equal to the square's side length.
To find the square's circumference, we need the sum of all 4 triangle bases, which is 4 times the square's side length.
Let x be the square's side length. Since the triangle base is x, the hypotenuse (using the Pythagorean theorem) is √(x^2 + (x/2)^2) = √(5x^2/4).
We know the triangle's circumference is 1, so 3 * √(5x^2/4) = 1. Solving for x, we get x = √(4/15).
Finally, the square's circumference is 4x = 4√(4/15), approximately 1.53.
Therefore, in Scenario 2, the square's circumference is 4√(4/15), approximately 1.53.
These are just two examples, and the actual circumference can vary depending on the specific division of the square.
In conclusion, without additional information about how the square is divided, the question cannot be definitively answered.