Answer:
Option B, 14.6 units
Step-by-step explanation:
Step 1: Find the distance of AB
[tex]AB =[/tex] [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
[tex]AB =[/tex] [tex]\sqrt{(3 - 1)^2 + (5 - 3)^2}[/tex]
[tex]AB =[/tex] [tex]\sqrt{(2)^2 + (2)^2}[/tex]
[tex]AB =[/tex] [tex]2\sqrt{2}[/tex] or 2.83...
Step 2: Find the distance of BC
[tex]BC =[/tex] [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
[tex]BC = \sqrt{(3 -1)^2 + (-1 - 3)^2}[/tex]
[tex]BC = \sqrt{(2)^2 + (-4)^2}[/tex]
[tex]BC = \sqrt{4 + 16}[/tex]
[tex]BC = \sqrt{20}[/tex]
[tex]BC = 2\sqrt{5}[/tex] or 4.47...
Step 3: Find the perimeter
AB is the same as AD and BC is the same as DC
[tex]2(AB) + 2(BC)[/tex]
[tex]2(2.83) + 2(4.47)[/tex]
[tex]5.66 + 8.94[/tex]
14.6 units
Answer: Option B, 14.6 units
