We would calculate the distance between the vertices by applying the formula for calculating the distance between two points which is expressed as
distance = √(x2 - x1)^2 + (y2 - y1)^2
Considering (1,-4) and (-5,0),
x1 = 1, y1 = - 4
x2 = - 5, y2 = 0
Distance = √(- 5 - 1)^2 + (0 - - 4)^2 = √(- 6)^2 + (4)^2 = √52 = 2√13
Considering (-5,0),and (-2,-9),
x1 = - 5, y1 = 0
x2 = - 2, y2 = - 9
Distance = √(- 2 - - 5)^2 + (- 9 - 0)^2 = √(- 2 + 5)^2 + (- 9)^2 = √90 = 3√10
Considering (1,-4) and (-2,-9),
x1 = 1, y1 = - 4
x2 = - 2, y2 = - 9
Distance = √(- 2 - 1)^2 + (- 9 - - 4) = √(- 3)^2 + (- 5)^2 = √34
Perimeter = sum of the length of each side
Perimeter = 2√13 + 3√10 + √34