Question

A walkway forms one diagonal of a square playground. The walkway is 14 m long. How long is a side of the​ playground?
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Part 1
Each side of the playground is
  
enter your response here m.
​(Round to the nearest meter as​ needed.)

Answer 1

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**.