Derrick built a pen for his dog using one side of his house. He has 28 feet of fencing to use for the three sides of his fence. Make a table that uses the distances d away from the house as input and the length of the side opposite the house and the area as outputs. Have at least 5 lines in your table.
To create the table, we need to calculate the length of the side opposite the house and the area for different distances away from the house.
Since we have limited fencing of 28 feet, we can assume that two sides of the pen will have the same length, opposite to the house. Let's call this length "x". The remaining side will be the side of the house, which is not fenced.
Now, let's create the table using different values for the distance "d" away from the house. We will calculate the length of the side opposite the house and the area for each distance.
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| Distance (d) | Opposite Side Length (x) | Area of the Pen |
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| 5 feet | 9 feet | 45 sq. ft. |
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| 8 feet | 10 feet | 40 sq. ft. |
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| 10 feet | 9.333 feet | 46.665 sq. ft.|
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| 12 feet | 9 feet | 54 sq. ft. |
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| 15 feet | 8 feet | 60 sq. ft. |
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To calculate the values in the table, we can use the following formulas:
1. Opposite Side Length (x) = (28 - 2d) / 2
2. Area of the Pen = d * x
By plugging in different values for "d" in the formulas above, we can calculate the corresponding values for the opposite side length (x) and the area of the pen.