A rectangle has a length of 13 and a width of 6. What is the perimeter of the rectangle?

1. TRANSLATE the problem information

• Given information:
  • Rectangle has length = \(\mathrm{13}\)
  • Rectangle has width = \(\mathrm{6}\)
  • Need to find perimeter

• What this tells us: The rectangle has two sides of length \(\mathrm{13}\) and two sides of length \(\mathrm{6}\)

2. INFER the approach

• Perimeter means the distance around the entire shape
• For a rectangle, this means adding up all four sides
• Since opposite sides are equal, we have: length + length + width + width

3. Calculate the perimeter

• Add all four sides: \(\mathrm{13 + 13 + 6 + 6}\)
• Combine like terms:
  \(\mathrm{(13 + 13) + (6 + 6)}\)
  \(\mathrm{= 26 + 12}\)
  \(\mathrm{= 38}\)

Answer: C. 38

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students misunderstand what "perimeter" means and only add two sides instead of all four.

Some students might think perimeter means adding just the length and width once (\(\mathrm{13 + 6 = 19}\)), or they might add only the two lengths (\(\mathrm{13 + 13 = 26}\)) or only the two widths (\(\mathrm{6 + 6 = 12}\)). When they see their calculation of \(\mathrm{26}\) matches choice B, or \(\mathrm{12}\) matches choice A, they select these incorrect answers without realizing they haven't found the complete perimeter.

This may lead them to select Choice A (12) if they only add the widths, or Choice B (26) if they only add the lengths.

Second Most Common Error:

Conceptual confusion about rectangle properties: Students might mistakenly think all four sides of the rectangle are the same length.

If they assume all sides equal \(\mathrm{13}\) (confusing rectangle with square), they would calculate \(\mathrm{13 \times 4 = 52}\), leading them to select Choice D (52).

The Bottom Line:

This problem tests whether students truly understand that perimeter means "all the way around" and that rectangles have two pairs of equal opposite sides. The key insight is methodically accounting for all four sides, not just the two given dimensions.