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*provide details with your answer if its NECESSARY. * What is the perimeter of this triangle?

*provide details with your answer if its NECESSARY. * What is the perimeter of this-example-1
User Lothar
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2 Answers

4 votes
27 units that’s the answer
User Stephenkelzer
by
8.6k points
4 votes

Answer:

27.9 units

Option B is the correct answer.

Explanation:

Finding the distance between the points A and B

A ( 3 , - 1 ) → ( x1 , y1 )

B ( 9 , - 5 )→ ( x2 , y2 )

Distance =
\sqrt{ {(x2 - x1)}^(2) + {(y2 - y1)}^(2) }


= \sqrt{ {(9 - 3)}^(2) + {( - 5 - ( - 1)}^(2) }


= \sqrt{ {(9 - 3)}^(2) + {( - 5 + 1))}^(2) }


= \sqrt{ {6}^(2) +( - 4) ^(2) }


= √(36 + 16)


= √(52)


= 2 √(13)

Finding the distance between the points B and C

B ( 9 , - 5 ) → ( x1 , y1 )

C ( 16 , - 2 )→ ( x2 , y2 )

Distance =
\sqrt{ {(x2 - x1)}^(2) + {(y2 - y1)}^(2) }


= \sqrt{ {(16 - 9)}^(2) + { (- 2 - ( - 5))}^(2) }


= \sqrt{ {(16 - 9)}^(2) + { ( - 2 + 5)}^(2) }


= \sqrt{ {7}^(2) + {(3)}^(2) }


= √(49 + 9)


= √(58) units

Finding the distance between the points A and C

A ( 3 , - 1 )→ ( x1 , y1 )

C ( 16 , - 2 )→ ( x2 , y2 )

Distance =
\sqrt{ {(x2 - x1)}^(2) + {(y2 - y1)}^(2) }


= \sqrt{ {(16 - 3)}^(2) + {( - 2 - ( - 1))}^(2) }


= \sqrt{ {(16 - 3)}^(2) + ( - 2 + 1) ^(2) }


= \sqrt{ {13}^(2) + ( { - 1)}^(2) }


= √(169 + 1)


= √(170) units

Now, let's find the perimeter:

Perimeter = AB + BC + AC

plug the values


= 2 √(13) + √(58) + √(170)

Calculate


= 27.9 units

Hope this helps..

Best regards!!

*provide details with your answer if its NECESSARY. * What is the perimeter of this-example-1
User Dparker
by
8.2k points

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