For this case we have that by definition, the distance between two points is given by:
[tex]d = \sqrt {(y2-y1) ^ 2 + (x2-x1) ^ 2}[/tex]
We find the distance AB:
[tex]A: (3,4)\\B: (- 5, -2)[/tex]
[tex]AB = \sqrt {(x2-x1) ^ 2 + (y2-y1) ^ 2}\\AB = \sqrt {(- 5-3) ^ 2 + (- 2-4) ^ 2}\\AB = \sqrt {(- 8) ^ 2 + (- 6) ^ 2}\\AB = \sqrt {64 + 36}\\AB = \sqrt {100}\\AB = 10[/tex]
We have the BC distance:
[tex]B: (- 5, -2)\\C: (5, -2)[/tex]
[tex]BC = \sqrt {(5 - (- 5)) ^ 2 + (- 2 - (- 2)) ^ 2}\\BC = \sqrt {(5 + 5) ^ 2 + (- 2 + 2) ^ 2}\\BC = \sqrt {(10) ^ 2 + (0) ^ 2}\\BC = \sqrt {100}\\BC = 10[/tex]
We find the CA distance:
[tex]C: (5, -2)\\A: (3,4)[/tex]
[tex]CA = \sqrt {(3-5) ^ 2 + (4 - (- 2)) ^ 2}CA = \sqrt {(- 2) ^ 2 + (4 + 2) ^ 2}\\CA = \sqrt {4 + 36}\\CA = \sqrt {40}\\CA = \sqrt {4 * 10}\\CA = 2 \sqrt {10}[/tex]
Thus, the perimeter is given by:
[tex]10 + 10 + 2 \sqrt {10} = 20 + 2 \sqrt {10}[/tex]
ANswer:
[tex]20 + 2 \sqrt {10}[/tex]
