Problem:Square X has a side length of 12 centimeters. The perimeter of square Y is 2 times the perimeter of...

1. TRANSLATE the problem information

• Given information:
  • Square X has side length = 12 cm
  • Perimeter of square Y = 2 × (perimeter of square X)
  • Need to find: side length of square Y

2. INFER the approach

• We need to work in stages: find X's perimeter → find Y's perimeter → find Y's side length
• This requires using the perimeter formula twice: once forward, once backward

3. Calculate the perimeter of square X

• Using \(\mathrm{P = 4s}\): \(\mathrm{P_X = 4(12) = 48}\) cm

4. TRANSLATE to find Y's perimeter

• "2 times the perimeter of square X" means: \(\mathrm{P_Y = 2 \times 48 = 96}\) cm

5. SIMPLIFY to find Y's side length

• We know \(\mathrm{P_Y = 96}\) and \(\mathrm{P = 4s}\) for any square
• So: \(\mathrm{96 = 4s}\)
• Divide both sides by 4: \(\mathrm{s = 24}\) cm

Answer: D. 24

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misinterpret "2 times the perimeter of square X" as "2 times the side length of square X"

They calculate: Side of Y = \(\mathrm{2 \times 12 = 24}\), but then think this IS the final answer without checking it makes sense with perimeter relationships. Or they might calculate \(\mathrm{2 \times 12 = 24}\), then think they need to do something else with it, leading to confusion.

This may lead them to select Choice D (24) for the wrong reasoning, or get confused and guess other answers.

Second Most Common Error:

Poor SIMPLIFY execution: Students correctly find that square Y has perimeter 96 cm, but make arithmetic errors when solving \(\mathrm{96 = 4s}\)

They might calculate \(\mathrm{96 \div 4}\) incorrectly, especially if rushing, or set up the division wrong.

This causes them to get stuck or select Choice A (6) or Choice C (14) from calculation errors.

The Bottom Line:

This problem tests whether students can follow a multi-step logical chain while carefully translating English phrases into correct mathematical relationships. The key insight is recognizing that you must work with perimeters first, not jump directly to side lengths.