Final answer:
To calculate the perimeter of the given triangle, distances between the given points are determined using the distance formula. After computing, the perimeter sums to 15.9 units, which does not match any of the provided options, suggesting a potential error in the question or its options.
Step-by-step explanation:
The perimeter of a triangle with coordinates at (3,0), (4,6), and (5,3) can be found by calculating the distance between each pair of points, which are the sides of the triangle, and then summing those distances.
Let's use the distance formula d = √((x2 - x1)^2 + (y2 - y1)^2) to find the lengths of the sides.
For side A (between (3,0) and (4,6)), we have:
√((4 - 3)^2 + (6 - 0)^2) = √(1^2 + 6^2) = √(1 + 36) = √37 ≈9.1
For side B (between (4,6) and (5,3)), we have:
√((5 - 4)^2 + (3 - 6)^2) = √(1^2 + (-3)^2) = √(1 + 9) = √10 ≈3.2
For side C (between (5,3) and (3,0)), we have:
√((5 - 3)^2 + (3 - 0)^2) = √(2^2 + 3^2) = √(4 + 9) = √13 ≈3.6
Summing the lengths of sides A, B, and C, we get the perimeter of the triangle:
9.1 + 3.2 + 3.6 = 15.9
Therefore, the correct answer, which has been rounded to the nearest tenth, is 15.9 units, which is not one of the options provided. It seems there may have been an error either in the calculation or in the provided options.