Let's solve the given problem, step by step:
Given:
- The area of the rectangular field is 3996.614 square meters.
- The length of the field is 72.35 meters.
### (i) Finding the Breadth
To find the breadth of the rectangular field, we use the formula for the area of a rectangle:
[tex]\[ \text{Area} = \text{Length} \times \text{Breadth} \][/tex]
Rearrange the formula to solve for the breadth:
[tex]\[ \text{Breadth} = \frac{\text{Area}}{\text{Length}} \][/tex]
Substitute the given values into the formula:
[tex]\[ \text{Breadth} = \frac{3996.614 \,\text{m}^2}{72.35 \,\text{m}} \][/tex]
After performing the division:
[tex]\[ \text{Breadth} = 55.24 \,\text{m} \][/tex]
So, the breadth of the field is 55.24 meters.
### (ii) Finding the Perimeter
To find the perimeter of the rectangular field, we use the formula for the perimeter of a rectangle:
[tex]\[ \text{Perimeter} = 2 \times (\text{Length} + \text{Breadth}) \][/tex]
Substitute the values of length and breadth:
[tex]\[ \text{Perimeter} = 2 \times (72.35 \,\text{m} + 55.24 \,\text{m}) \][/tex]
First, calculate the sum of length and breadth:
[tex]\[ 72.35 \,\text{m} + 55.24 \,\text{m} = 127.59 \,\text{m} \][/tex]
Then multiply by 2:
[tex]\[ \text{Perimeter} = 2 \times 127.59 \,\text{m} \][/tex]
[tex]\[ \text{Perimeter} = 255.18 \,\text{m} \][/tex]
So, the perimeter of the field is 255.18 meters.
### Summary
(i) The breadth of the field is 55.24 meters.
(ii) The perimeter of the field is 255.18 meters.
