The square of the diagonal of a square is 50 sq. units. Find the side of the square.

Answer

To find the side of the square given that the square of the diagonal is 50 square units, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**: We know that the square of the diagonal (d) of a square is given as 50 square units. We need to find the length of one side (s) of the square.

2. **Use the Relationship Between the Diagonal and the Side**: In a square, the relationship between the side (s) and the diagonal (d) can be expressed using the Pythagorean theorem. The diagonal of a square can be calculated as:
\[ d = s\sqrt{2} \]

3. **Square the Diagonal**: Since we know that the square of the diagonal is given as 50, we can write:
\[ d^2 = (s\sqrt{2})^2 \]
Simplifying this gives:
\[ d^2 = s^2 \cdot 2 \]

4. **Set the Equation**: Now, we can set the equation using the value of \(d^2\):
\[ s^2 \cdot 2 = 50 \]

5. **Solve for \(s^2\)**: To isolate \(s^2\), divide both sides by 2:
\[ s^2 = \frac{50}{2} = 25 \]

6. **Find \(s\)**: Now, take the square root of both sides to find the value of \(s\):
\[ s = \sqrt{25} = 5 \]

7. **Conclusion**: Therefore, the length of one side of the square is:
\[ \text{Side of the square} = 5 \text{ units} \]