**Problem:**
The diagonal of a square is 12√2 cm. Find its perimeter.

**Solution:**
To find the perimeter of the square, we need to know the length of one side of the square. Since the diagonal is given, we can use the properties of a square to find the length of the side.

1. **Properties of a Square:**
- A square is a quadrilateral with all four sides equal in length.
- The diagonals of a square are perpendicular bisectors of each other.
- The diagonals of a square are congruent (i.e., have the same length).

2. **Using the Diagonal to Find the Side Length:**
- Let's assume the side length of the square is 's' cm.
- We can use the Pythagorean theorem to relate the side length and the diagonal of the square.
- According to the Pythagorean theorem, in a right-angled triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
- In this case, the diagonal of the square acts as the hypotenuse, and the sides of the square act as the other two sides of the triangle.
- Thus, we have the equation: s^2 + s^2 = (12√2)^2.
- Simplifying this equation, we get: 2s^2 = 288.
- Dividing both sides by 2, we have: s^2 = 144.
- Taking the square root of both sides, we find: s = √144 = 12 cm.

3. **Calculating the Perimeter:**
- Now that we know the side length of the square is 12 cm, we can calculate its perimeter.
- The perimeter of a square is the sum of all its four sides.
- In this case, the perimeter of the square is 4 * 12 cm = 48 cm.

**Answer:**
The perimeter of the square is 48 cm.

Let the side of a square = a cm

The diagonal of a square = 12√2 cm

a√2 = 12√2 cm

a = (12√2)/√2 cm

a = 12 cm

The perimeter of a square = 4 * side

= (4 * 12) cm

= 48 cm ( Ans)