A rectangular garden has an area of 72 square feet. If the length of the garden is 9 feet, what...

1. TRANSLATE the problem information

• Given information:
  • Area of rectangular garden = 72 square feet
  • Length = 9 feet
• Find: width of the garden

2. INFER the approach

• Since we know area and length, we need the area formula for rectangles
• We'll substitute the known values and solve for the unknown width

3. Set up the equation using the area formula

• \(\mathrm{Area = length \times width}\)
• \(\mathrm{72 = 9 \times width}\)

4. SIMPLIFY to find the width

• Divide both sides by 9: \(\mathrm{width = 72 \div 9 = 8}\) feet

Answer: 8 feet (Choice B)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY execution: Students make arithmetic errors when dividing 72 ÷ 9

Some students might incorrectly calculate this division, perhaps getting 6 or 12 instead of 8. This computational mistake would lead them to select Choice A (6) or Choice D (12).

Second Most Common Error:

Poor TRANSLATE reasoning: Students confuse what they're solving for

Students might see that the length is 9 feet and simply select that value without recognizing they need to find the width. This confusion about which dimension they're looking for may lead them to select Choice C (9).

The Bottom Line:

This problem tests whether students can set up and solve a basic equation using the rectangle area formula. The main challenge is maintaining accuracy through the translation and arithmetic steps.