Final answer:
The perimeter of triangle ABC with given vertices is approximately 17.62 units, which after rounding is closest to 18 units, making the correct answer b) 18 units.
Step-by-step explanation:
To find the perimeter of triangle ABC with vertices A(5,4), B(5, -3), and C(2,4), we need to calculate the lengths of the sides of the triangle using the distance formula. The distance between two points (x1,y1) and (x2,y2) is given by the formula √[(x2-x1)² + (y2-y1)²].
First, we find the distance between points A and B:
√[(5-5)² + (4-(-3))²] = √[0² + 7²] = 7 units.
Next, the distance between points A and C:
√[(5-2)² + (4-4)²] = √[3² + 0²] = 3 units.
Finally, the distance between points B and C:
√[(5-2)² + (-3-4)²] = √[3² + (-7)²] = √[9 + 49] = √[58] ≈ 7.62 units.
The perimeter is the sum of these distances:
Perimeter = AB + AC + BC = 7 + 3 + 7.62 ≈ 17.62 units.
Therefore, the correct answer, after rounding, is b) 18 units.