A rectangle has a length of 3 units and a width of 39 units. Which expression gives the area, in...

1. TRANSLATE the problem information

• Given information:
  • Rectangle has \(\mathrm{length = 3\;units}\)
  • Rectangle has \(\mathrm{width = 39\;units}\)
  • Need to find expression for area in square units

2. INFER the approach

• To find area of a rectangle, we multiply \(\mathrm{length \times width}\)
• This means we need the expression: \(\mathrm{3 \times 39}\)

3. Evaluate the answer choices

• Check each option against our area expression:
  • A. \(\mathrm{2(3 + 39)}\): This adds the dimensions then doubles it - that's the perimeter formula
  • B. \(\mathrm{2(3 \times 39)}\): This multiplies the dimensions then doubles it - that's twice the area
  • C. \(\mathrm{3 + 39}\): This just adds the dimensions - not area
  • D. \(\mathrm{3 \times 39}\): This multiplies the dimensions - exactly what we need for area

Answer: D. \(\mathrm{3 \times 39}\)

Why Students Usually Falter on This Problem

Most Common Error Path:

Conceptual confusion about area vs. perimeter: Students mix up the formulas for area and perimeter of rectangles.

They remember that rectangles involve adding and multiplying the dimensions, but can't recall which operation goes with which measurement. Since choice A shows \(\mathrm{2(3 + 39)}\), they might think "that looks like a rectangle formula" without recognizing it's actually the perimeter formula (2 times the sum of length and width).

This may lead them to select Choice A (\(\mathrm{2(3 + 39)}\)).

The Bottom Line:

This problem tests whether students can distinguish between area (multiply the dimensions) and perimeter (add the dimensions, then double). The key insight is remembering that area always involves multiplication of dimensions, while perimeter involves addition.