Find the perimeter of the polygon using the distance formula of Triangle ABC with vertices A(3, 5), B(3, 1), C(0, 1)

AB = sqrt((3-3)² + (1-5)²) = sqrt(9+16) = 5

BC = sqrt((0-3)² + (1-1)²) = sqrt(9+0) = 3
CA = sqrt((0-3)² + (1-5)²) = sqrt(9+16) = 5

Take it from here.

To find the perimeter of the triangle ABC, you need to find the lengths of all of its sides and then add them together.

The distance formula can be used to calculate the length of a line segment in a coordinate plane. It is given by:

d = √((x2 - x1)^2 + (y2 - y1)^2)

Let's calculate the lengths of the sides of triangle ABC:

Side AB:
Coordinates of A = (3, 5)
Coordinates of B = (3, 1)
Using the distance formula:
d_AB = √((3 - 3)^2 + (1 - 5)^2)
= √(0^2 + (-4)^2)
= √(0 + 16)
= √16
= 4

Side BC:
Coordinates of B = (3, 1)
Coordinates of C = (0, 1)
Using the distance formula:
d_BC = √((0 - 3)^2 + (1 - 1)^2)
= √((-3)^2 + 0^2)
= √(9 + 0)
= √9
= 3

Side CA:
Coordinates of C = (0, 1)
Coordinates of A = (3, 5)
Using the distance formula:
d_CA = √((3 - 0)^2 + (5 - 1)^2)
= √(3^2 + 4^2)
= √(9 + 16)
= √25
= 5

Now that we have the lengths of all three sides, we can calculate the perimeter of the triangle:

Perimeter of ABC = AB + BC + CA
= 4 + 3 + 5
= 12

Therefore, the perimeter of triangle ABC is 12 units.