To find the length of each side of a square field given its area, we follow a logical sequence of calculations:
1. Understanding the Area Given:
The area of the square field is given as [tex]\(80 \frac{244}{729}\)[/tex] square meters. To handle this mixed number more easily, let's convert it into a single decimal or fraction.
2. Convert the Mixed Number to a Decimal:
[tex]\( 80 \frac{244}{729} \)[/tex] can be expressed as [tex]\( 80 + \frac{244}{729} \)[/tex]. We need to divide 244 by 729 and then add this result to 80.
[tex]\[
\frac{244}{729} \approx 0.33470507544582
\][/tex]
Therefore,
[tex]\[
80 + 0.33470507544582 = 80.33470507544582
\][/tex]
So, the area of the square field is approximately [tex]\( 80.33470507544582 \)[/tex] square meters.
3. Finding the Length of Each Side:
The area of a square is found using the formula:
[tex]\[
\text{Area} = \text{side length}^2
\][/tex]
Let's denote the side length by [tex]\( s \)[/tex]. Thus:
[tex]\[
s^2 = 80.33470507544582
\][/tex]
4. Solving for the Side Length:
To find the side length [tex]\( s \)[/tex], we take the square root of both sides.
[tex]\[
s = \sqrt{80.33470507544582}
\][/tex]
5. Calculate the Square Root:
By calculating the square root, we find:
[tex]\[
s \approx 8.962962962962962
\][/tex]
Hence, the length of each side of the field is approximately [tex]\( 8.962962962962962 \)[/tex] meters.
