Question

a walkway forms one diagonal of a square playground. the walkway is 12 m long. how long is a side of the playground? each side of the playground is \\(\square\\) m. (round to the nearest meter as needed.)

Explanation:

Step1: Recall square diagonal formula

For a square with side length \( s \), the diagonal \( d \) is related by \( d = s\sqrt{2} \).

Step2: Solve for side length \( s \)

Given \( d = 12 \) m, we have \( 12 = s\sqrt{2} \). So \( s=\frac{12}{\sqrt{2}} \). Rationalize the denominator: \( s = \frac{12\sqrt{2}}{2}=6\sqrt{2}\approx6\times1.414 = 8.484 \).

Step3: Round to nearest meter

Rounding \( 8.484 \) to the nearest meter gives \( 8 \).

Answer:

8