ProblemA rectangular garden has a length of 15 meters and a width of 8 meters. If you want to build...

1. TRANSLATE the problem information

• Given information:
  • Rectangular garden with length = 15 meters
  • Width = 8 meters
  • Need to find how much fencing is required "around the entire perimeter"

• What this tells us: We need to find the perimeter (total distance around the outside)

2. INFER the mathematical approach

• Since we need the distance around a rectangle, we must use the perimeter formula
• The perimeter formula accounts for all four sides: 2 lengths + 2 widths

3. Apply the perimeter formula

• SIMPLIFY the calculation:
  • \(\mathrm{Perimeter = 2(length + width)}\)
  • \(\mathrm{Perimeter = 2(15 + 8)}\)
  • \(\mathrm{Perimeter = 2(23) = 46}\) meters

Answer: B) 46 meters

Why Students Usually Falter on This Problem

Most Common Error Path:

Conceptual confusion: Mixing up area and perimeter formulas

Students sometimes think "rectangle problem" and immediately multiply \(\mathrm{length \times width = 15 \times 8 = 120}\). They forget that fencing goes around the outside (perimeter), not covering the inside space (area).

This leads them to select Choice C (120 meters).

Second Most Common Error:

Weak INFER reasoning: Not recognizing that rectangles have four sides

Some students add \(\mathrm{length + width = 15 + 8 = 23}\), forgetting that rectangles have two lengths and two widths. They don't make the connection that you need to double this sum.

This may lead them to select Choice A (23 meters).

The Bottom Line:

The key insight is distinguishing between "around" (perimeter) versus "covering" (area), and remembering that rectangles have four sides, not just two.