To solve for the perimeter of triangle ABC, I'll first extract the coordinates of points A, B, and C from the image:

• Point A is located at $(4, 5)$
• Point B is located at $(1, 2)$
• Point C is located at $(7, 2)$

The perimeter of the triangle is the sum of the lengths of its sides. We can calculate the length of each side using the distance formula: $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Step 1: Calculate the length of side AB

Using the coordinates of points A and B: $AB = \sqrt{(4 - 1)^2 + (5 - 2)^2} = \sqrt{3^2 + 3^2} = \sqrt{9 + 9} = \sqrt{18} = 3\sqrt{2} \approx 4.24$

Step 2: Calculate the length of side AC

Using the coordinates of points A and C: $AC = \sqrt{(4 - 7)^2 + (5 - 2)^2} = \sqrt{(-3)^2 + 3^2} = \sqrt{9 + 9} = \sqrt{18} = 3\sqrt{2} \approx 4.24$

Step 3: Calculate the length of side BC

Using the coordinates of points B and C: $BC = \sqrt{(7 - 1)^2 + (2 - 2)^2} = \sqrt{6^2 + 0^2} = \sqrt{36} = 6$

Step 4: Calculate the perimeter

The perimeter $P$ is the sum of the lengths of the sides: $P = AB + AC + BC = 4.24 + 4.24 + 6 = 14.48$

So, the perimeter of triangle ABC is approximately 14.48 units.

Would you like more details on any step, or do you have any questions?

Related Questions:

1. What is the area of triangle ABC using its coordinates?
2. How would the perimeter change if the triangle were rotated?
3. What is the classification of triangle ABC (e.g., equilateral, isosceles, etc.)?
4. How do you find the midpoint of any of the sides of triangle ABC?
5. What is the slope of line AB, and how does it compare to the slope of line AC?

Tip:

When working with coordinate geometry, always double-check the signs and values of coordinates to avoid calculation errors!