A square has a diagonal length 12.what is the length of one of the sides of the square?

Solution:
1. Given:
- Diagonal length of the square: d = 12

2. Use the relationship between the side length s of the square and the diagonal d:
- For a square, the diagonal is the hypotenuse of a right triangle formed by two sides of the square. Hence, using the Pythagorean theorem, we have:
s^2 + s^2 = d^2
- Simplify:
2s^2 = d^2

3. Solve for s:
- Substitute d = 12:
2s^2 = 12^2
2s^2 = 144

4. Divide both sides by 2:
s^2 = 72

5. Take the square root of both sides:
s = \sqrt{72}
s = \sqrt{36 \times 2} = 6\sqrt{2}

The length of one side of the square is 6\sqrt{2} units.