In a square, the relationship between the length of a diagonal and the length of a side can be described using the Pythagorean theorem. For a square with side length \( s \), the length of the diagonal \( d \) is given by the formula:
\[ d = s \sqrt{2} \]
In this case, we know the diagonal \( d \) is 14 m. We can set up the equation:
\[ 14 = s \sqrt{2} \]
To solve for \( s \), divide both sides by \( \sqrt{2} \):
\[ s = \frac{14}{\sqrt{2}} \]
To make it easier to work with, let's rationalize the denominator:
\[ s = \frac{14 \sqrt{2}}{2} = 7 \sqrt{2} \]
Now calculate \( 7 \sqrt{2} \):
\[ 7 \sqrt{2} \approx 7 \times 1.414 \approx 9.899 \]
Rounding to the nearest meter, we get:
\[ s \approx 10 \text{ m} \]
Thus, each side of the playground is approximately 10 m.