Final answer:
The perimeter of triangle ABC is found by using the distance formula to calculate the lengths of sides AB, BC, and CA, and then summing these lengths.
Step-by-step explanation:
The student has asked for the perimeter of a triangle with vertices A(2, 8), B(16, 2), and C(6, 2). To calculate this, we need to find the lengths of the sides of the triangle, which can be done using the distance formula between two points: √((x2-x1)² + (y2-y1)²).
The length of side AB is √((16-2)² + (2-8)²) = √(196 + 36) = √232.
The length of side BC is √((6-16)² + (2-2)²) = √(100 + 0) = √100.
The length of side CA is √((2-6)² + (8-2)²) = √(16 + 36) = √52.
To find the perimeter, we add the lengths of all three sides:
Perimeter = AB + BC + CA
= √232 + √100 + √52
= √232 + 10 + √52.
Calculating the square roots and summing the lengths give us the perimeter of ∆ABC.