It looks like you've mentioned a rectangle with vertices at the coordinates \((1,2)\), \((1,6)\), \((5,6)\), and \((5,2)\).
However, you've also asked for the perimeter of a triangle, which cannot be formed from these four points directly since they represent a rectangle.
If we need to find the perimeter of the rectangle itself instead of a triangle, we can do that as follows.
To find the perimeter of the rectangle:
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Calculate the lengths of two adjacent sides:
- The length between the points \((1,2)\) and \((1,6)\) (the vertical side) is: \[ 6 - 2 = 4 \text{ units} \]
- The length between the points \((1,2)\) and \((5,2)\) (the horizontal side) is: \[ 5 - 1 = 4 \text{ units} \]
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The perimeter \(P\) of a rectangle is given by the formula: \[ P = 2 \times (\text{length} + \text{width}) \] Here, both the length and width are \(4\): \[ P = 2 \times (4 + 4) = 2 \times 8 = 16 \text{ units} \]
Thus, the perimeter of the rectangle is \(16\) units.
If you intended to find the perimeter of a triangle formed by some of these vertices, please clarify which three points should be used. But based on the given coordinates as mentioned, the perimeter of the rectangle is approximately 16.0 units.
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