What is the perimeter, in inches, of a rectangle with a length of 4 inches and a width of 9...

1. TRANSLATE the problem information

• Given information:
  • Rectangle with length = 4 inches
  • Rectangle with width = 9 inches
  • Need to find: perimeter (distance around the outside)

2. INFER what perimeter means for a rectangle

• Perimeter = sum of ALL sides of the figure
• A rectangle has 4 sides: 2 equal lengths and 2 equal widths
• So we need: length + length + width + width

3. Calculate the perimeter

• Add all four sides: \(4 + 4 + 9 + 9 = 26\) inches
• Or use the formula:
  \(\mathrm{P} = 2\mathrm{l} + 2\mathrm{w}\)
  \(\mathrm{P} = 2(4) + 2(9)\)
  \(\mathrm{P} = 8 + 18\)
  \(\mathrm{P} = 26\) inches

Answer: D. 26

Why Students Usually Falter on This Problem

Most Common Error Path:

Conceptual confusion about perimeter: Students think perimeter means just adding the length and width once, rather than understanding it means the total distance around the entire rectangle.

This leads them to calculate: \(4 + 9 = 13\) inches

This may lead them to select Choice A (13)

Second Most Common Error:

Weak INFER reasoning about counting sides: Students partially understand they need more than just l + w, but incorrectly count the sides - either using two lengths + one width, or one length + two widths.

• Two lengths + one width: \(4 + 4 + 9 = 17\) → Choice B (17)
• One length + two widths: \(4 + 9 + 9 = 22\) → Choice C (22)

The Bottom Line:

This problem tests whether students truly understand that perimeter means "all the way around" - requiring them to count every single side of the rectangle, not just mention each dimension once.