Answer: Choice B) 15.7
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Explanation:
Use the distance formula to find the distance from point A to point B
[tex]A = (x_1,y_1) = (5,5) \text{ and } B = (x_2, y_2) = (7,3)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(5-7)^2 + (5-3)^2}\\\\d = \sqrt{(-2)^2 + (2)^2}\\\\d = \sqrt{4 + 4}\\\\d = \sqrt{8}\\\\d \approx 2.8284\\\\[/tex]
This means segment AB is approximately 2.8284 units long.
Repeat those similar steps to find the following other side lengths:
Side note: this figure is a parallelogram with congruent pairs of opposite sides
Now add up the four exterior sides to get the perimeter
perimeter = AB+BC+CD+AD
perimeter = 2.8284+5+2.8284+5
perimeter = 15.6568
perimeter = 15.7 units
