The width of a rectangle is 7 centimeters. The length of the rectangle is 40 centimeters longer than the width....

1. TRANSLATE the problem information

• Given information:
  • Width = 7 cm
  • Length is "40 centimeters longer than the width"
  • Need to find area in square cm

• What "40 centimeters longer than the width" means:
  \(\mathrm{Length = width + 40 = 7 + 40}\)

2. SIMPLIFY to find the length

• \(\mathrm{Length = 7 + 40 = 47}\) cm

3. INFER what to do next

• Now we have both dimensions: width = 7 cm, length = 47 cm
• To find area, we need to multiply length times width

4. SIMPLIFY to find the area

• \(\mathrm{Area = length \times width = 47 \times 7 = 329}\) square cm

Answer: D. 329

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misinterpret "40 centimeters longer than the width" and might think the length is simply 40 cm, or they get confused about what calculation to perform.

Some students might calculate \(\mathrm{7 \times 40 = 280}\) instead of first finding that \(\mathrm{length = 7 + 40 = 47}\), then multiplying \(\mathrm{47 \times 7}\). This leads to an answer not among the choices, causing confusion and guessing.

Second Most Common Error:

Incomplete solution process: Students might correctly find that length = 47 cm but then forget they need to calculate the area. They might think 47 is the final answer, but since 47 isn't among the choices, they might select the closest number or just guess.

The Bottom Line:

This problem requires careful reading to correctly translate the relationship between length and width, followed by systematic application of the area formula. Students who rush through the translation step or stop before completing the full calculation process will struggle to find the correct answer.