Answer:
27.9 units
Option B is the correct answer.
Step-by-step explanation:
Finding the distance between the points A and B
A ( 3 , - 1 ) → ( x1 , y1 )
B ( 9 , - 5 )→ ( x2 , y2 )
Distance = [tex] \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } [/tex]
[tex] = \sqrt{ {(9 - 3)}^{2} + {( - 5 - ( - 1)}^{2} } [/tex]
[tex] = \sqrt{ {(9 - 3)}^{2} + {( - 5 + 1))}^{2} } [/tex]
[tex] = \sqrt{ {6}^{2} +( - 4) ^{2} } [/tex]
[tex] = \sqrt{36 + 16} [/tex]
[tex] = \sqrt{52} [/tex]
[tex] = 2 \sqrt{13} [/tex]
Finding the distance between the points B and C
B ( 9 , - 5 ) → ( x1 , y1 )
C ( 16 , - 2 )→ ( x2 , y2 )
Distance = [tex] \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } [/tex]
[tex] = \sqrt{ {(16 - 9)}^{2} + { (- 2 - ( - 5))}^{2} } [/tex]
[tex] = \sqrt{ {(16 - 9)}^{2} + { ( - 2 + 5)}^{2} } [/tex]
[tex] = \sqrt{ {7}^{2} + {(3)}^{2} } [/tex]
[tex] = \sqrt{49 + 9} [/tex]
[tex] = \sqrt{58} [/tex] units
Finding the distance between the points A and C
A ( 3 , - 1 )→ ( x1 , y1 )
C ( 16 , - 2 )→ ( x2 , y2 )
Distance = [tex] \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } [/tex]
[tex] = \sqrt{ {(16 - 3)}^{2} + {( - 2 - ( - 1))}^{2} } [/tex]
[tex] = \sqrt{ {(16 - 3)}^{2} + ( - 2 + 1) ^{2} } [/tex]
[tex] = \sqrt{ {13}^{2} + ( { - 1)}^{2} } [/tex]
[tex] = \sqrt{169 + 1} [/tex]
[tex] = \sqrt{170} [/tex] units
Now, let's find the perimeter:
Perimeter = AB + BC + AC
plug the values
[tex] = 2 \sqrt{13} + \sqrt{58} + \sqrt{170} [/tex]
Calculate
[tex] = 27.9[/tex] units
Hope this helps..
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