A square garden has an area of 2025 square feet. A fence is to be built around the entire perimeter...

1. TRANSLATE the problem information

• Given information:
  • Square garden has area of 2025 square feet
  • Need fencing for entire perimeter

• What this tells us: We have area, need perimeter

2. INFER the solution approach

• To find perimeter of a square, we need the side length first
• We can get side length from the area using the area formula
• Then apply perimeter formula

3. SIMPLIFY to find the side length

• Use area formula: \(\mathrm{A = s^2}\)
• Substitute: \(\mathrm{s^2 = 2025}\)
• Take square root: \(\mathrm{s = \sqrt{2025} = 45}\) feet

4. SIMPLIFY to find the perimeter

• Use perimeter formula: \(\mathrm{P = 4s}\)
• Substitute: \(\mathrm{P = 4(45) = 180}\) feet

Answer: 180

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students might try to find perimeter directly from area without recognizing they need to find the side length as an intermediate step.

This leads to confusion about how area (2025) relates to perimeter, causing them to get stuck and guess randomly among the choices.

Second Most Common Error:

Poor SIMPLIFY execution: Students correctly set up \(\mathrm{s^2 = 2025}\) but make calculation errors, thinking \(\mathrm{\sqrt{2025}}\) = something other than 45.

If they calculate the side length incorrectly, their final perimeter will be wrong. For example, if they somehow get \(\mathrm{s = 22.5}\), then \(\mathrm{P = 4(22.5) = 90}\), leading them to select Choice A (90).

The Bottom Line:

This problem tests whether students can connect area and perimeter through the intermediate step of finding side length. The key insight is that you cannot go directly from area to perimeter - you must find the side length first.