To find the length of the diagonal for a square with a side length of [tex]\(2\sqrt{2}\)[/tex] meters, we can follow these steps:
1. Understand the ratio:
The ratio of the side of a square to its diagonal is [tex]\(1:\sqrt{2}\)[/tex]. This implies the diagonal [tex]\(d\)[/tex] of the square can be calculated using the side length [tex]\(s\)[/tex] with the formula:
[tex]\[
d = s \sqrt{2}
\][/tex]
2. Given side length:
The side length [tex]\(s\)[/tex] of the square is [tex]\(2\sqrt{2}\)[/tex] meters.
3. Calculate the diagonal:
Substitute the side length into the formula to find the diagonal:
[tex]\[
d = (2\sqrt{2}) \times \sqrt{2}
\][/tex]
4. Simplify the expression:
[tex]\[
d = 2 \times \sqrt{2} \times \sqrt{2} = 2 \times 2 = 4 \text{ meters}
\][/tex]
Therefore, the length of the diagonal for a square with a side length of [tex]\(2\sqrt{2}\)[/tex] meters is exactly [tex]\(4\)[/tex] meters.
