The area of a rectangle is 630 square inches. The length of the rectangle is 70 inches. What is the...

1. TRANSLATE the problem information

• Given information:
  • Area = 630 square inches
  • Length = 70 inches
  • Need to find: width

• This tells us we have two of the three measurements needed for the area formula

2. INFER the approach

• Since we know area and length, we can use the rectangle area formula to find width
• The area formula \(\mathrm{A = length × width}\) can be rearranged to solve for any missing variable

3. TRANSLATE into mathematical equation

• Using \(\mathrm{A = length × width}\): \(\mathrm{630 = 70 × w}\)

4. SIMPLIFY to solve for width

• Divide both sides by 70: \(\mathrm{w = 630 ÷ 70 = 9}\)
• Check: \(\mathrm{70 × 9 = 630}\) ✓

Answer: A (9 inches)

Why Students Usually Falter on This Problem

Most Common Error Path:

Missing conceptual knowledge: Not remembering or incorrectly applying the rectangle area formula

Students might perform random operations with the given numbers instead of using the systematic relationship \(\mathrm{A = ℓw}\). For example, they might divide the area by 2 (\(\mathrm{630 ÷ 2 = 315}\)) or subtract the length from the area (\(\mathrm{630 - 70 = 560}\)), leading them to select Choice C (315) or Choice D (560).

Second Most Common Error:

Weak TRANSLATE reasoning: Misidentifying what the problem is asking for

Some students correctly use the area formula but then provide the length (70) as their final answer instead of the calculated width (9). This leads them to select Choice B (70).

The Bottom Line:

This problem tests whether students can systematically apply the rectangle area formula rather than guessing with random calculations. Success requires both remembering the formula and carefully tracking which measurement they're solving for.