Question:A rectangular floor has an area of 1,344 square feet. If the length of the floor is 48 feet, what...

1. TRANSLATE the problem information

• Given information:
  • Area of rectangular floor = 1,344 square feet
  • Length of floor = 48 feet
  • Find: width of floor

2. INFER the approach

• Since we know the area and length of a rectangle, we can use the area formula to find the missing width
• The strategy is to substitute known values into Area = length × width, then solve for the unknown

3. Set up the equation using the rectangle area formula

• \(\mathrm{Area = length \times width}\)
• \(\mathrm{1,344 = 48 \times width}\)

4. SIMPLIFY to solve for width

• To isolate width, divide both sides by the length:
• \(\mathrm{width = 1,344 \div 48}\)
• \(\mathrm{width = 28}\) (use calculator)

5. Include units in final answer

• The width of the floor is 28 feet

Answer: 28

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students may set up the equation incorrectly, thinking they need to multiply area and length rather than divide. They might write: \(\mathrm{width = 1,344 \times 48}\), leading to an enormously large answer like 64,512. This conceptual misunderstanding about how to manipulate the area formula causes them to move in the wrong direction entirely.

Second Most Common Error:

Poor SIMPLIFY execution: Students set up the equation correctly but make calculation errors when performing \(\mathrm{1,344 \div 48}\). Common arithmetic mistakes might lead them to answers like 26 or 32, causing them to select an incorrect choice if multiple choice options are available.

The Bottom Line:

This problem tests whether students can work backward from a formula they know well. The key insight is recognizing that when you know two of the three values in \(\mathrm{Area = length \times width}\), you can always find the third through basic algebra - but you must be careful about which operation to use.