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Let's take a look at the table and the calculations. It appears that Adam is trying to calculate the area and perimeter of different rectangular fences, with different lengths and widths.

The formula for perimeter is:  
\[
\text{Perimeter} = 2 \times (\text{Length} + \text{Width})
\]
The formula for area is:  
\[
\text{Area} = \text{Length} \times \text{Width}
\]

It seems like the perimeter is the same for each arrangement at 160 feet. This suggests that the total length of the fence is constant, and the length and width vary to fit that total.

Let's go through the calculations:

1. For the first row:
   - Length: 10 ft, Width: 70 ft
   - Perimeter: \( 2 \times (10 + 70) = 160 \, \text{ft} \) (correct)
   - Area: \( 10 \times 70 = 700 \, \text{ft}^2 \) (correct)

2. For the second row:
   - Length: 20 ft, Width: 60 ft
   - Perimeter: \( 2 \times (20 + 60) = 160 \, \text{ft} \) (correct)
   - Area: \( 20 \times 60 = 1200 \, \text{ft}^2 \) (needs adjustment in your notes)

3. For the third row:
   - Length: 30 ft, Width: 50 ft
   - Perimeter: \( 2 \times (30 + 50) = 160 \, \text{ft} \) (correct)
   - Area: \( 30 \times 50 = 1500 \, \text{ft}^2 \) (correct)

4. For the fourth row:
   - Length: 40 ft, Width: 40 ft
   - Perimeter: \( 2 \times (40 + 40) = 160 \, \text{ft} \) (correct)
   - Area: \( 40 \times 40 = 1600 \, \text{ft}^2 \) (correct)

5. For the fifth row:
   - Length: 50 ft, Width: 30 ft
   - Perimeter: \( 2 \times (50 + 30) = 160 \, \text{ft} \) (correct)
   - Area: \( 50 \times 30 = 1500 \, \text{ft}^2 \) (correct)

6. For the sixth row:
   - Length: 60 ft, Width: 20 ft
   - Perimeter: \( 2 \times (60 + 20) = 160 \, \text{ft} \) (correct)
   - Area: \( 60 \times 20 = 1200 \, \text{ft}^2 \) (correct)

7. For the seventh row:
   - Length: 70 ft, Width: 10 ft
   - Perimeter: \( 2 \times (70 + 10) = 160 \, \text{ft} \) (correct)
   - Area: \( 70 \times 10 = 700 \, \text{ft}^2 \) (correct)

Your numbers are very close, but the area for the second row should be 1200 square feet instead of 200 square feet. The adjustments in your notes show some calculations that are incorrect, so I recommend revising them to match the proper area calculations.

Would you like me to walk through how to adjust these calculations for each row?

Fill in Adam’s table with all of the arrangements for the fence. (The first one is done for you.)

Learn how to calculate the perimeter and area of rectangular fences with different length and width combinations. This problem helps students understand how to apply the formulas for perimeter and area in real-world scenarios, suitable for Grades 5-7.

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