Final answer:
The perimeter of triangle ABC is calculated using the distance formula for each side. After finding the lengths of sides AB, BC, and CA, they are summed to get the perimeter, which is approximately 20.42 units.
Step-by-step explanation:
To calculate the perimeter of triangle ABC with the given vertices, we need to find the lengths of its sides using the distance formula, which is derived from the Pythagorean theorem. The distance formula for points (x1, y1) and (x2, y2) is:
Distance = √((x2 - x1)² + (y2 - y1)²).
Applying this formula, we first calculate the distances between the points A, B, and C:
- Side AB: √((-5 - 4)² + (3 - 5)²) = √(81 + 4) = √85 ≈ 9.22 units
- Side BC: √((4 - 5)² + (5 - 5)²) = √(1 + 0) = 1 unit
- Side CA: √((-5 - 5)² + (3 - 5)²) = √(100 + 4) = √104 ≈ 10.20 units
The perimeter is the sum of the lengths of these sides:
Perimeter = AB + BC + CA ≈ 9.22 + 1 + 10.20 ≈ 20.42 units.
Therefore, the perimeter of triangle ABC is about 20.42 units.