Answer: 187 feet
This value is approximate.
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Explanation:
The cable is connected by these key points
- A = (0,3)
- B = (6,5)
- C = (12,4)
- D = (18,2)
Let's use the distance formula to find the length of segment AB.
[tex]A = (x_1,y_1) = (0,3)\\\\B = (x_2,y_2) = (6,5)\\\\d = \text{Distance from A to B} = \text{length of segment AB}\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(0-6)^2 + (3-5)^2}\\\\d = \sqrt{(-6)^2 + (-2)^2}\\\\d = \sqrt{36 + 4}\\\\d = \sqrt{40}\\\\d \approx 6.325\\\\[/tex]
Segment AB is roughly 6.325 units long. You could use the pythagorean theorem as an alternative route instead of the distance formula.
If you repeated this process for the other segment lengths, then you should get these other approximate lengths.
Add up those three results:
AB+BC+CD = 6.325+6.083+6.325 = 18.733
The entire cable is roughly 18.733 units long.
Since 1 unit = 10 feet, we'll multiply that result by 10.
18.733*10 = 187.33 feet
This rounds to 187 feet which is the approximate length of the cable.
