The given function \(\mathrm{f(x) = 2x + 244}\) represents the perimeter, in centimeters (cm), of a rectangle with a length...

1. TRANSLATE the problem information

• Given information:
  • \(\mathrm{f(x) = 2x + 244}\) represents the perimeter in cm
  • The rectangle has length x cm and a fixed width
  • Need to find the width in cm

2. INFER the mathematical relationship

• Since we know this is a rectangle's perimeter, we can use the perimeter formula
• For a rectangle: \(\mathrm{Perimeter = 2(length + width) = 2 \times length + 2 \times width}\)
• If the width is w, then: \(\mathrm{Perimeter = 2x + 2w}\)
• Since both expressions represent the same perimeter, we can set them equal

3. SIMPLIFY by setting up and solving the equation

• Set the expressions equal: \(\mathrm{2x + 2w = 2x + 244}\)
• Subtract 2x from both sides: \(\mathrm{2w = 244}\)
• Divide both sides by 2: \(\mathrm{w = 122}\)

Answer: B. 122

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students may not connect the word problem to the rectangle perimeter formula. They might see \(\mathrm{f(x) = 2x + 244}\) and think the width is simply the constant term 244, not recognizing that they need to use the perimeter formula structure.

This may lead them to select Choice C (244).

Second Most Common Error:

Poor INFER reasoning: Students might recognize they need the perimeter formula but fail to set up the correct equation. They may think the coefficient 2 in front of x represents the width directly, rather than understanding it comes from 2 × length in the perimeter formula.

This may lead them to select Choice A (2).

The Bottom Line:

This problem requires students to bridge between a function notation and a geometric formula. The key insight is recognizing that the given function must match the standard rectangle perimeter formula, allowing you to solve for the unknown width parameter.