A rectangle has a perimeter of 28 centimeters and a length of 9 centimeters. What is the width of the...

1. TRANSLATE the problem information

• Given information:
  • Perimeter = 28 centimeters
  • Length = 9 centimeters
  • Need to find: width

• This translates to the equation: \(\mathrm{28 = 2(9 + width)}\)

2. SIMPLIFY to solve for width

• Start with: \(\mathrm{28 = 2(9 + width)}\)
• Divide both sides by 2: \(\mathrm{14 = 9 + width}\)
• Subtract 9 from both sides: \(\mathrm{width = 5}\)

3. Verify the answer makes sense

• Check: \(\mathrm{P = 2(9 + 5) = 2(14) = 28}\) ✓

Answer: B (5 centimeters)

Why Students Usually Falter on This Problem

Most Common Error Path:

Missing conceptual knowledge: Students forget that perimeter involves going around the entire rectangle, so both length AND width get counted twice.

Instead of using \(\mathrm{P = 2(length + width)}\), they might think \(\mathrm{P = length + width}\), leading to:

\(\mathrm{28 = 9 + width}\)
\(\mathrm{width = 19}\)

This leads them to select Choice D (19).

Second Most Common Error:

Weak SIMPLIFY execution: Students make arithmetic mistakes when solving the equation.

Common errors include:

• Forgetting to divide by 2: getting \(\mathrm{28 - 9 = 19}\) directly
• Addition/subtraction errors: \(\mathrm{28 \div 2 = 14}\), but then \(\mathrm{14 + 9}\) instead of \(\mathrm{14 - 9}\)

These arithmetic slips can lead to selecting Choice C (10) or other incorrect values.

The Bottom Line:

This problem tests whether students truly understand what "perimeter" means for rectangles - that you travel around the entire shape, counting each side. The algebra is straightforward once the setup is correct, but conceptual confusion about perimeter leads to the most serious errors.