Certainly, students. Let's solve this problem step-by-step to find the perimeter of a square land given its area.
1. Understanding the Problem:
- We are given the area of a square land, which is 9,409 square meters.
- Our task is to find the perimeter of this square.
2. Finding the Side Length:
- For any square, the area ([tex]\(A\)[/tex]) is given by the formula:
[tex]\[
A = s^2
\][/tex]
where [tex]\(s\)[/tex] is the length of one side of the square.
- We need to rearrange this formula to solve for [tex]\(s\)[/tex]:
[tex]\[
s = \sqrt{A}
\][/tex]
- Substituting the given area into the formula:
[tex]\[
s = \sqrt{9,409}
\][/tex]
3. Calculating the Side Length:
- Taking the square root of 9,409:
[tex]\[
s = 97 \text{ meters}
\][/tex]
- So, the length of one side of the square is 97 meters.
4. Finding the Perimeter:
- The perimeter ([tex]\(P\)[/tex]) of a square is given by the formula:
[tex]\[
P = 4s
\][/tex]
- Substituting the side length we calculated:
[tex]\[
P = 4 \times 97
\][/tex]
[tex]\[
P = 388 \text{ meters}
\][/tex]
Hence, the perimeter of the square land is 388 meters.
