Certainly! Let's solve these two questions step-by-step:
### Question 14:
Given:
- There are 3600 soldiers.
- Each row has as many soldiers as there are rows.
To Find:
- The number of rows.
Solution:
1. Let [tex]\( n \)[/tex] be the number of rows.
2. Since each row has the same number of soldiers as the number of rows, if there are [tex]\( n \)[/tex] rows, then each row will have [tex]\( n \)[/tex] soldiers.
3. Therefore, the total number of soldiers will be [tex]\( n \)[/tex] rows [tex]\(\times\)[/tex] [tex]\( n \)[/tex] soldiers per row, i.e., [tex]\( n \times n = n^2 \)[/tex].
4. We know the total number of soldiers is 3600.
5. So, we set up the equation:
[tex]\[
n^2 = 3600
\][/tex]
6. To find [tex]\( n \)[/tex], we take the square root of both sides:
[tex]\[
n = \sqrt{3600}
\][/tex]
7. Therefore, the number of rows [tex]\( n \)[/tex] is:
[tex]\[
n = 60
\][/tex]
So, the number of rows is 60.
---
### Question 15:
Given:
- The area of a square is 6889 m².
To Find:
- The perimeter of the square.
Solution:
1. Let [tex]\( s \)[/tex] be the side length of the square.
2. The formula for the area of a square is given by:
[tex]\[
\text{Area} = s^2
\][/tex]
3. Given that the area is 6889 m², we can write:
[tex]\[
s^2 = 6889
\][/tex]
4. To find [tex]\( s \)[/tex], we take the square root of both sides:
[tex]\[
s = \sqrt{6889}
\][/tex]
5. This gives us the side length [tex]\( s \)[/tex] as:
[tex]\[
s = 83
\][/tex]
6. Now, the perimeter [tex]\( P \)[/tex] of a square is given by:
[tex]\[
P = 4 \times \text{side length}
\][/tex]
7. Substituting the value of [tex]\( s \)[/tex]:
[tex]\[
P = 4 \times 83
\][/tex]
8. Therefore, the perimeter [tex]\( P \)[/tex] is:
[tex]\[
P = 332 \, \text{m}
\][/tex]
So, the perimeter of the square is 332 meters.
---
### Summary of answers:
- The number of rows in Question 14 is 60.
- The perimeter of the square in Question 15 is 332 meters.
