Answer
Perimeter of ABC = 10 + 2√5 = 10 + 4.47 = 14.47
Step-by-step explanation
The perimeter of a figure is given as the sum of the exterior sides of the triangle.
The distance between two points with the coordinates (x₁, y₁) and (x₂, y₂) is given as
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
Starting with AB, A (0, 0) and B (-3, -4)
AB = √[(x₂ - x₁)² + (y₂ - y₁)²]
AB = √[(-3 - 0)² + (-4 - 0)²]
AB = √[(-3)² + (-4)²]
AB = √[9 + 16]
AB = √[25] = 5
Going to BC, B (-3, -4) and C (-5, 0)
BC = √[(x₂ - x₁)² + (y₂ - y₁)²]
BC = √[(-5 - (-3))² + (0 - (-4))²]
BC = √[(-5 + 3)² + (0 + 4)²]
BC = √[(-2)² + (4)]
BC = √[4 + 16] = √20 = 2√5
Going to AC, A (0, 0) and C (-5, 0)
AC = √[(x₂ - x₁)² + (y₂ - y₁)²]
AC = √[(-5 - 0)² + (0 - 0)²]
AC = √[(-5)² + (0)²]
AC = √[25 + 0]
AC = √[25] = 5
Perimeter of ABC
= AB + BC + AC
= 5 + 2√5 + 5
= 10 + 2√5
Hope this Helps!!!