Final answer:
The perimeter of the triangle with vertices at (1, 5), (5, 8), and (8, 4) is found by calculating the length of each side using the distance formula and then summing them up to get 17.07 units.
Step-by-step explanation:
To determine the perimeter of a triangle with vertices at (1, 5), (5, 8), and (8, 4), we need to find the lengths of all three sides and then sum them. The distance between two points (x1, y1) and (x2, y2) in the coordinate plane is given by the formula √((x2 - x1)² + (y2 - y1)²). Let's calculate the lengths of the sides:
- Side 1 (between points (1, 5) and (5, 8)): Side length = √((5 - 1)² + (8 - 5)²) = √(16 + 9) = √25 = 5 units.
- Side 2 (between points (5, 8) and (8, 4)): Side length = √((8 - 5)² + (4 - 8)²) = √(9 + 16) = √25 = 5 units.
- Side 3 (between points (8, 4) and (1, 5)): Side length = √((1 - 8)² + (5 - 4)²) = √(49 + 1) = √50 = approximately 7.07 units (using three significant figures).
The perimeter of the triangle is the sum of these side lengths: 5 units + 5 units + 7.07 units = 17.07 units.
Note: It is important to use the same unit of measurement for all sides and express the final answer to the appropriate number of significant figures.