To find the perimeter of rectangle EFGH, we first need to determine the lengths of its sides.
The vertices of rectangle EFGH are:
- E(6, 9)
- F(4, 9)
- G(4, -5)
- H(6, -5)
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Calculate the length of side EF: Since E and F have the same y-coordinate, the distance between them can be found using the x-coordinates: \[ EF = |x_E - x_F| = |6 - 4| = 2 \]
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Calculate the length of side EH: Since E and H have the same x-coordinate, the distance between them can be found using the y-coordinates: \[ EH = |y_E - y_H| = |9 - (-5)| = |9 + 5| = |14| = 14 \]
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Find the perimeter of rectangle EFGH: The perimeter \( P \) of a rectangle can be calculated using the formula: \[ P = 2(\text{length} + \text{width}) = 2(EF + EH) \] Substituting the side lengths we found: \[ P = 2(2 + 14) = 2 \times 16 = 32 \]
Thus, the perimeter of rectangle EFGH is \( \boxed{32} \).