To find the perimeter of rectangle ABCD, we first need to calculate the lengths of its sides.
Given the vertices:
- A(1, 7)
- B(4, 7)
- C(4, -4)
- D(1, -4)
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Calculate the length of side AB: Since A and B share the same y-coordinate, the length can be calculated by finding the difference in the x-coordinates: \[ AB = |x_B - x_A| = |4 - 1| = 3 \]
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Calculate the length of side AD: Since A and D share the same x-coordinate, the length can be calculated by finding the difference in the y-coordinates: \[ AD = |y_A - y_D| = |7 - (-4)| = |7 + 4| = 11 \]
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Calculate the perimeter: The perimeter \(P\) of a rectangle is given by the formula: \[ P = 2 \times (length + width) \] In this case, the length \(AB = 3\) and the width \(AD = 11\): \[ P = 2 \times (3 + 11) = 2 \times 14 = 28 \]
Thus, the perimeter of rectangle ABCD is \(\boxed{28}\).