Question

Find the Perimeter of Triangle ABC with vertices A(-2,1), B(5,2), C(4,8).

A. 24 units
B. 27 units
C. 29 units
D. 30 units

Answer 1

To find the perimeter of triangle ABC, we need to calculate the length of each side using the distance formula and then add them together.

Step-by-step explanation:

To find the perimeter of triangle ABC, we need to find the length of each side and then add them together. Using the distance formula, we can calculate the length of side AB as:

DAB = sqrt((x2 - x1)2 + (y2 - y1)2)

DAB = sqrt((5 - (-2))2 + (2 - 1)2) = sqrt(49 + 1) = sqrt(50)

Similarly, we can find the lengths of sides BC and AC. Then, we can add the three side lengths together to find the perimeter:

Perimeter = DAB + DBC + DAC = sqrt(50) + sqrt((4 - 5)2 + (8 - 2)2) + sqrt((-2 - 4)2 + (1 - 8)2)

Perimeter = sqrt(50) + sqrt(1 + 36) + sqrt(36 + 49) ≈ 10.3 + 6.2 + 12.1 = 28.6

Therefore, the perimeter of triangle ABC is approximately 28.6 units.