A rectangular poster has an area of 360 square inches. A copy of the poster is made in which the...

1. TRANSLATE the problem information

• Given information:
  • Original poster area = 360 square inches
  • Copy has length and width each increased by 20%
  • Need to find the area of the copy

• What "increased by 20%" means: multiply the original dimension by 1.2

2. INFER the relationship between original and copy

• Since \(\mathrm{area} = \mathrm{length} \times \mathrm{width}\) for any rectangle, we can work with the original area without knowing the specific dimensions
• If original length = \(\mathrm{ℓ}\) and width = \(\mathrm{w}\), then \(\mathrm{ℓw} = 360\)
• Copy dimensions become: length = \(1.2\mathrm{ℓ}\) and width = \(1.2\mathrm{w}\)

3. INFER how the area changes

• Copy area = \((1.2\mathrm{ℓ}) \times (1.2\mathrm{w})\)
• \(= 1.2 \times 1.2 \times \mathrm{ℓw}\)
• \(= 1.44 \times \mathrm{ℓw}\)
• Since \(\mathrm{ℓw} = 360\), the copy area = \(1.44 \times 360\)

4. SIMPLIFY to find the final answer

• Copy area = \(1.44 \times 360 = 518.4\) square inches (use calculator)

Answer: 518.4 square inches

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misinterpret "each increased by 20%" and apply the 20% increase directly to the area instead of to each dimension.

They think: "Area increases by 20%, so new area = \(360 + 0.20(360) = 360 + 72 = 432\)"

This leads them to get 432 as their answer, missing the key insight that when both dimensions increase by 20%, the area increases by much more than 20%.

Second Most Common Error:

Poor SIMPLIFY execution: Students correctly understand that each dimension becomes 1.2 times larger but make calculation errors.

Common mistakes include: calculating \(1.2 \times 1.2\) as 2.4 instead of 1.44, or making arithmetic errors when computing \(1.44 \times 360\).

This leads to various incorrect numerical answers and causes them to second-guess their approach.

The Bottom Line:

This problem tests whether students understand that area scaling isn't linear - when you increase both dimensions of a rectangle by the same percentage, the area increases by the square of that factor. The key insight is recognizing that a 20% increase in each dimension results in a 44% increase in area (since \(1.2^2 = 1.44\)).