Answer
The perimeter of the triangle is 48.298 units
Explanation
The triangle has the vertices (-9, -5), (-6, 1) and (5, 8).
To find the perimeter of the triangle, we need to find the lengths of the sides of the triangle. The perimeter is the sum of all its sides.
Each side will be calculated from the distance between the vertices.
The distance between two points with the coordinates (x₁, y₁) and (x₂, y₂) is given as
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
The sides of the triangle will be between
(-9, -5) and (-6, 1)
(-9, -5) and (5, 8)
(-6, 1) and (5, 8)
(x₁, y₁) and (x₂, y₂) is (-9, -5) and (-6, 1)
x₁ = -9
y₁ = -5
x₂ = -6
y₂ = 1
d = √[(-6 - (-9))² + (1 - (-5))²]
d = √[(-15)² + (6)²]
d = √(261)
d = 16.155
(x₁, y₁) and (x₂, y₂) is (-9, -5) and (5, 8)
x₁ = -9
y₁ = -5
x₂ = 5
y₂ = 8
d = √[(5 - (-9))² + (8 - (-5))²]
d = √[(14)² + (13)²]
d = √(365)
d = 19.105
(x₁, y₁) and (x₂, y₂) is (-6, 1) and (5, 8)
x₁ = -6
y₁ = 1
x₂ = 5
y₂ = 8
d = √[(5 - (-6))² + (8 - 1)²]
d = √[(11)² + (7)²]
d = √(170)
d = 13.038
The perimeter of the triangle is thus given as
Perimeter = 16.155 + 19.105 + 13.038
= 48.298 units
Hope this Helps!!!
