If the length of a diagonal of square is 6cm. Find the length of the side of the square.

Answer

To find the length of the side of a square when the length of the diagonal is given, we can use the Pythagorean theorem. Here’s a step-by-step solution:

### Step 1: Understand the relationship between the diagonal and the sides of the square.
In a square, if we denote the length of each side as \( a \), the diagonal \( d \) can be calculated using the Pythagorean theorem. The diagonal forms a right triangle with two sides of the square. Thus, we have:
\[ d = \sqrt{a^2 + a^2} \]
This simplifies to:
\[ d = \sqrt{2a^2} = a\sqrt{2} \]

### Step 2: Substitute the given diagonal length into the equation.
We know from the problem that the length of the diagonal \( d \) is 6 cm. Therefore, we can set up the equation:
\[ 6 = a\sqrt{2} \]

### Step 3: Solve for \( a \).
To find \( a \), we can rearrange the equation:
\[ a = \frac{6}{\sqrt{2}} \]

### Step 4: Simplify the expression for \( a \).
To simplify \( \frac{6}{\sqrt{2}} \), we can multiply the numerator and the denominator by \( \sqrt{2} \):
\[ a = \frac{6\sqrt{2}}{2} = 3\sqrt{2} \]

### Step 5: Write the final answer with the appropriate unit.
Thus, the length of each side of the square is:
\[ a = 3\sqrt{2} \text{ cm} \]