Explanation:
Let's use the Pythagorean Theorem to find the length of one side of the square.
The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the diagonal of the square is the hypotenuse of a right triangle, and the two sides are the sides of the square. Let's call the length of one side of the square "s".
Using the Pythagorean Theorem, we get:
s^2 + s^2 = 12^2
2s^2 = 144
s^2 = 72
s = √72
s ≈ 8.49
Now that we know the length of one side of the square, we can find the perimeter by multiplying by 4 (since all four sides of a square have the same length):
Perimeter = 4s
Perimeter = 4(√72)
Perimeter ≈ 33.96 cm
Therefore, the perimeter of the square with a diagonal of length 12 cm is approximately 33.96 cm.