A rectangular floor has an area of 48 square feet. If the length of the floor is 8 feet, what...

1. TRANSLATE the problem information

• Given information:
  • Area of rectangular floor = 48 square feet
  • Length of floor = 8 feet
  • Need to find: Perimeter of floor

2. INFER the solution strategy

• To find perimeter, I need both length and width
• I have length (8 feet) but need to find width
• Since I know area and length, I can use the area formula to find width first

3. SIMPLIFY to find the width

• Use \(\mathrm{Area = length \times width}\)
• Substitute known values: \(\mathrm{48 = 8 \times width}\)
• Solve for width: \(\mathrm{width = 48 \div 8 = 6\text{ feet}}\)

4. SIMPLIFY to find the perimeter

• Use \(\mathrm{P = 2(length + width)}\)
• Substitute values: \(\mathrm{P = 2(8 + 6)}\)
• Calculate: \(\mathrm{P = 2(14) = 28\text{ feet}}\)

Answer: C (28)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students attempt to find perimeter directly without realizing they need both dimensions first. They may try to use area in place of width in the perimeter formula, leading to nonsensical calculations.

This may lead them to select Choice D (56) by incorrectly adding area and length (48 + 8 = 56), thinking this gives perimeter.

Second Most Common Error:

Conceptual confusion about formulas: Students find the width correctly (6 feet) but then use an incorrect perimeter formula. They calculate length + width = 8 + 6 = 14, forgetting to multiply by 2.

This may lead them to select Choice B (14).

Third Most Common Error:

Incomplete solution: Students correctly find width = 6 feet but stop there, thinking this is the final answer.

This may lead them to select Choice A (6).

The Bottom Line:

Success requires recognizing this as a two-step problem: use area to find the missing dimension first, then apply the perimeter formula. Students who try shortcuts or mix up formulas will select incorrect answers.