Sure! Let’s solve the problem step by step.
1. Understanding the Problem:
- We are given the area of a square garden, which is [tex]\( 676.208016 \)[/tex] square meters.
- We need to find the length of railing required to fence the garden. This corresponds to finding the perimeter of the square.
2. Step-by-Step Solution:
- Since the garden is square-shaped, all four sides of the garden have equal length.
- Let’s denote the side length of the square as [tex]\( s \)[/tex].
- The formula for the area [tex]\( A \)[/tex] of a square is:
[tex]\[
A = s^2
\][/tex]
- We are given the area [tex]\( A = 676.208016 \)[/tex] square meters. Thus, we need to find [tex]\( s \)[/tex]:
[tex]\[
s^2 = 676.208016
\][/tex]
- To find [tex]\( s \)[/tex], we take the square root of the area:
[tex]\[
s = \sqrt{676.208016}
\][/tex]
- From the problem, the square root of [tex]\( 676.208016 \)[/tex] is found to be:
[tex]\[
s = 26.004 \, \text{meters}
\][/tex]
- Now, to find the perimeter [tex]\( P \)[/tex] of the square garden, we use the formula for the perimeter of a square:
[tex]\[
P = 4s
\][/tex]
- Substituting [tex]\( s = 26.004 \)[/tex] meters into the perimeter formula:
[tex]\[
P = 4 \times 26.004 = 104.016 \, \text{meters}
\][/tex]
3. Conclusion:
- The length of the railing required to fence the garden is [tex]\( 104.016 \)[/tex] meters.
So, the detailed steps show that we first determine the side length of the square garden from the area and then use that to compute the perimeter, which gives us the required length of the railing.
