A rectangle has an area of 119 square centimeters. If the width of the rectangle is 7 centimeters, what is...

1. TRANSLATE the problem information

• Given information:
  • Rectangle area = 119 square centimeters
  • Width = 7 centimeters
  • Need to find: length

• This translates to: \(\mathrm{Area = length \times width}\), where \(\mathrm{119 = length \times 7}\)

2. INFER the solution strategy

• Since we know area and width, we can find length by rearranging the formula
• The area formula becomes: \(\mathrm{length = Area \div width}\)
• This means: \(\mathrm{length = 119 \div 7}\)

3. SIMPLIFY through calculation

• Calculate: \(\mathrm{119 \div 7 = 17}\)
• Therefore, \(\mathrm{length = 17}\) centimeters

Answer: C) 17 cm

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students may misinterpret the relationship between area, length, and width, thinking they should add the values instead of using multiplication in the area formula.

They might calculate something like \(\mathrm{119 - 7 = 112}\) or try \(\mathrm{119 + 7 = 126}\), leading to confusion since neither result matches any answer choice. This leads to guessing among the available options.

Second Most Common Error:

Poor SIMPLIFY execution: Students correctly set up \(\mathrm{119 \div 7}\) but make arithmetic errors in the division process.

Common miscalculations include thinking \(\mathrm{119 \div 7 = 14}\) (perhaps confusing with \(\mathrm{14 \times 7 = 98}\)) or getting distracted and selecting the width value itself. This may lead them to select Choice A (7 cm) or Choice B (14 cm).

The Bottom Line:

This problem requires students to work backwards from the area formula - they must recognize that when two of the three variables (area, length, width) are known, simple algebraic rearrangement will reveal the third. Success depends on solid conceptual understanding of the area formula combined with careful arithmetic execution.