To determine the length of a side of a square given that the diagonals measure 24 meters, we can follow these steps:
1. Understand the relationship:
- In a square, the length of the diagonal [tex]\( d \)[/tex] is related to the length of a side [tex]\( s \)[/tex] by the Pythagorean theorem. For any square, the equation will always be:
[tex]\[
d = s\sqrt{2}
\][/tex]
2. Given diagonal length:
- The diagonal [tex]\( d \)[/tex] is given as 24 meters.
3. Rearrange the formula to solve for [tex]\( s \)[/tex]:
- We need to isolate [tex]\( s \)[/tex]. This can be done by dividing both sides of the equation by [tex]\( \sqrt{2} \)[/tex]:
[tex]\[
s = \frac{d}{\sqrt{2}}
\][/tex]
4. Substitute the given diagonal length into the formula:
- Substitute [tex]\( d = 24 \)[/tex] into the formula:
[tex]\[
s = \frac{24}{\sqrt{2}}
\][/tex]
5. Evaluate the expression:
- The length of the side of the square, [tex]\( s \)[/tex], can be calculated as:
[tex]\[
s \approx 16.97 \, \text{meters}
\][/tex]
Using this result, let's match it to the given options:
- [tex]\( \frac{10}{2} \approx 5.0 \, \text{meters} \)[/tex]
- [tex]\( \frac{24}{2} = 12.0 \, \text{meters} \)[/tex]
- [tex]\( 8\sqrt{2} \approx 11.31 \, \text{meters} \)[/tex]
- [tex]\( \frac{12}{2} = 6.0 \, \text{meters} \)[/tex]
The closest value corresponding to [tex]\( 16.97 \)[/tex] meters is [tex]\( 16.97 \, \text{meters} \)[/tex]. Let's ensure that we use the correct corresponding option that aligns with this.
Given these calculations, the length of a side of the square does not correspond to any of the options directly, so the side length obtained should be closest to [tex]\( 16.97 \, \text{meters} \)[/tex]. However, option (a), [tex]\( 8\sqrt{2} \)[/tex], can be considered as a less accurate representation if it were intended to simplify the result, but typically not correct.
