Each side of a square has a length of 45. What is the perimeter of this square?

1. TRANSLATE the problem information

• Given information:
  • We have a square
  • Each side has length 45
  • Need to find the perimeter
• What this tells us: We need to find the total distance around the square

2. INFER the approach

• Since perimeter means "distance around the outside," we need to add up all the side lengths
• A square has 4 equal sides, so we have four sides of length 45 each
• We can either add them directly (45 + 45 + 45 + 45) or use the formula \(\mathrm{P} = 4\mathrm{s}\)

3. SIMPLIFY the calculation

• Using addition: \(45 + 45 + 45 + 45 = 180\)
• Using formula: \(\mathrm{P} = 4(45) = 180\)

Answer: 180

Why Students Usually Falter on This Problem

Most Common Error Path:

Conceptual confusion about perimeter: Some students confuse perimeter with area and try to multiply \(45 \times 45 = 2,025\)

Students might think "perimeter" means the space inside the square rather than the distance around it. This leads to confusion and either guessing or attempting an area calculation.

Second Most Common Error:

Weak SIMPLIFY execution: Students understand the concept but make arithmetic errors, such as:

• Adding incorrectly: 45 + 45 + 45 + 45 = 160 (missing 20)
• Multiplying incorrectly: \(4 \times 45 = 160\) or \(4 \times 45 = 200\)

These calculation errors lead to selecting an incorrect answer if multiple choice options are close to the correct value.

The Bottom Line:

This problem tests whether students truly understand what "perimeter" means and can perform basic multiplication. The concept is straightforward, but students who confuse perimeter with area or make simple arithmetic errors will struggle.