Sure, let's break this down into two parts: finding the perimeter of the rectangular field and finding the side of a square garden given its perimeter.
### Part 1: Perimeter of the Rectangular Field
Given:
- Length of the rectangle (L) = 7 meters
- Width of the rectangle (W) = 30 centimeters
Step 1: Convert the width from centimeters to meters.
Since there are 100 centimeters in a meter:
[tex]\[ \text{Width in meters} = \frac{30 \text{ cm}}{100} = 0.3 \text{ meters} \][/tex]
Step 2: Apply the formula for the perimeter of a rectangle.
[tex]\[ \text{Perimeter of the rectangle} = 2 \times (L + W) \][/tex]
Step 3: Substitute the given dimensions into the formula.
[tex]\[ \text{Perimeter of the rectangle} = 2 \times (7 \text{ m} + 0.3 \text{ m}) \][/tex]
Step 4: Perform the addition inside the parentheses.
[tex]\[ 7 \text{ m} + 0.3 \text{ m} = 7.3 \text{ m} \][/tex]
Step 5: Multiply by 2 to find the perimeter.
[tex]\[ \text{Perimeter of the rectangle} = 2 \times 7.3 \text{ m} = 14.6 \text{ m} \][/tex]
So, the perimeter of the rectangular field is [tex]\( 14.6 \)[/tex] meters.
### Part 2: Side of a Square Garden Given Its Perimeter
Given:
- Perimeter of the square garden = 120 meters
Step 1: Apply the formula for the perimeter of a square.
[tex]\[ \text{Perimeter of the square} = 4 \times \text{side length} \][/tex]
Step 2: Solve for the side length.
[tex]\[ \text{side length} = \frac{\text{Perimeter}}{4} \][/tex]
Step 3: Substitute the given perimeter into the formula.
[tex]\[ \text{side length} = \frac{120 \text{ m}}{4} \][/tex]
Step 4: Perform the division.
[tex]\[ \text{side length} = 30 \text{ m} \][/tex]
Thus, the side of the square garden is [tex]\( 30 \)[/tex] meters.
### Summary
- The perimeter of the rectangular field is [tex]\( 14.6 \)[/tex] meters.
- The side of the square garden is [tex]\( 30 \)[/tex] meters.
