Triangle A'B'C' is similar to triangle ABC, where A, B, and C correspond to A', B', and C', respectively. In...

1. TRANSLATE the problem information

• Given information:
  • Triangle A'B'C' is similar to triangle ABC
  • A, B, and C correspond to A', B', and C', respectively
  • In triangle ABC: \(\mathrm{AB = 4}\) units, \(\mathrm{BC = 6}\) units, \(\mathrm{AC = 8}\) units
  • Each side of triangle A'B'C' is 3 times the length of the corresponding side in triangle ABC
  • Need to find: length of side A'B'
• What this tells us: We have a scale factor of 3 between the triangles

2. INFER the correspondence and approach

• Since A corresponds to A' and B corresponds to B', then side A'B' corresponds to side AB
• We can directly apply the scale factor to find A'B'

3. SIMPLIFY using the scale factor

• \(\mathrm{A'B' = scale\ factor \times corresponding\ side\ in\ original\ triangle}\)
• \(\mathrm{A'B' = 3 \times AB}\)
  \(\mathrm{= 3 \times 4}\)
  \(\mathrm{= 12\ units}\)

Answer: C. 12 units

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students may misinterpret which sides correspond to each other, particularly getting confused about the order of vertices in the correspondence.

Some students might think B'C' corresponds to AB (mixing up the vertex order), leading them to calculate \(\mathrm{B'C' = 3 \times 4 = 12}\) instead of recognizing that \(\mathrm{A'B' = 3 \times 4 = 12}\). However, since they still get 12, they would still select the correct answer by accident.

More problematically, students might get confused about which triangle has the scale factor applied and think ABC is 3 times larger than A'B'C', leading them to divide: \(\mathrm{A'B' = AB \div 3}\)
\(\mathrm{= 4 \div 3}\)
\(\mathrm{\approx 1.33\ units}\). This doesn't match any answer choice, leading to confusion and guessing.

The Bottom Line:

This problem tests your ability to correctly interpret the relationship between similar figures and identify corresponding parts. The key insight is carefully reading which triangle is scaled up from which, and matching the correct corresponding sides.