For this case, we have that the perimeter of the triangle will be given by the sum of its sides.
To find the measure of each side, we apply the formula of the distance between two points:
[tex]d = \sqrt {(x_ {2} -x_ {1}) ^ 2+ (y_ {2} -y_ {1}) ^ 2}[/tex]
AB side:
[tex]AB = \sqrt {(- 1-5) ^ 2 + (1 - (- 1)) ^ 2}\\AB = \sqrt {(- 6) ^ 2 + (2) ^ 2}\\AB = \sqrt {36 + 4}\\AB = \sqrt {40}\\AB = 6.3[/tex]
BC side:
[tex]BC = \sqrt {(0 - (- 1)) ^ 2 + (- 3-1) ^ 2}\\BC = \sqrt {(1) ^ 2 + (- 4) ^ 2}\\BC = \sqrt {1 + 16}\\BC = \sqrt {17}\\BC = 4.1[/tex]
CA side:
[tex]CA = \sqrt {(5-0) ^ 2 + (- 1 - (- 3)) ^ 2}\\CA = \sqrt {(5) ^ 2 + (2) ^ 2}\\CA = \sqrt {25 + 4}\\CA = \sqrt {29}\\CA = 5.4[/tex]
Thus, the perimeter of the figure is: 15.8
ANswer:
15.8
