To compute the perimeter of a parallelogram given its vertices, we need to find the lengths of its sides. The vertices provided are (2, 3), (6, 3), (7, 7), and (3, 7).
We'll first calculate the lengths of the sides by finding the distance between the pairs of vertices.
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Distance between (2, 3) and (6, 3): \[ d = \sqrt{(6 - 2)^2 + (3 - 3)^2} = \sqrt{4^2 + 0^2} = \sqrt{16} = 4 \]
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Distance between (6, 3) and (7, 7): \[ d = \sqrt{(7 - 6)^2 + (7 - 3)^2} = \sqrt{1^2 + 4^2} = \sqrt{1 + 16} = \sqrt{17} \approx 4.1 \]
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Distance between (7, 7) and (3, 7): \[ d = \sqrt{(3 - 7)^2 + (7 - 7)^2} = \sqrt{(-4)^2 + 0^2} = \sqrt{16} = 4 \]
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Distance between (3, 7) and (2, 3): \[ d = \sqrt{(2 - 3)^2 + (3 - 7)^2} = \sqrt{(-1)^2 + (-4)^2} = \sqrt{1 + 16} = \sqrt{17} \approx 4.1 \]
Now we can find the perimeter \( P \) of the parallelogram by adding the lengths of all four sides. Since opposite sides of a parallelogram are equal, we can simplify this calculation as follows: \[ P = 2 \times (4 + \sqrt{17}) \approx 2 \times (4 + 4.1) = 2 \times 8.1 = 16.2 \]
Therefore, the perimeter of the parallelogram is approximately 16.2 units.
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