To find the perimeter of the parallelogram with vertices at (2,1), (2,3), (4,4), and (4,2), we first need to find the lengths of its sides.
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Calculate the lengths of the sides.
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Side between (2,1) and (2,3): \[ \text{Length} = \sqrt{(2 - 2)^2 + (3 - 1)^2} = \sqrt{0 + 2^2} = \sqrt{4} = 2 \]
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Side between (2,3) and (4,4): \[ \text{Length} = \sqrt{(4 - 2)^2 + (4 - 3)^2} = \sqrt{2^2 + 1^2} = \sqrt{4 + 1} = \sqrt{5} \approx 2.2 \]
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Side between (4,4) and (4,2): \[ \text{Length} = \sqrt{(4 - 4)^2 + (2 - 4)^2} = \sqrt{0 + (-2)^2} = \sqrt{4} = 2 \]
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Side between (4,2) and (2,1): \[ \text{Length} = \sqrt{(2 - 4)^2 + (1 - 2)^2} = \sqrt{(-2)^2 + (-1)^2} = \sqrt{4 + 1} = \sqrt{5} \approx 2.2 \]
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Sum the lengths of the sides to find the perimeter. Each pair of opposite sides has the same length:
\[ \text{Perimeter} = 2 + \sqrt{5} + 2 + \sqrt{5} = 4 + 2\sqrt{5} \]
Using \(\sqrt{5} \approx 2.236\):
\[ 2\sqrt{5} \approx 2 \times 2.236 \approx 4.472 \]
Therefore, the perimeter is:
\[ \text{Perimeter} \approx 4 + 4.472 \approx 8.472 \]
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Round to the nearest tenth:
The total perimeter, rounded to the nearest tenth, is approximately:
\[ \text{Perimeter} \approx 8.5 \]
Thus, the perimeter of the parallelogram is approximately 8.5 units.
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