A square has a perimeter of 144. What is the length of one side of this square?

1. TRANSLATE the problem information

• Given information:
  • Perimeter of the square = 144
  • Need to find: length of one side
• What this tells us: We need to use the relationship between a square's perimeter and its side length.

2. TRANSLATE the mathematical relationship

• Since a square has 4 equal sides, if we call one side \(\mathrm{s}\), then:
  • Perimeter = \(\mathrm{s + s + s + s = 4s}\)
  • So our equation becomes: \(\mathrm{4s = 144}\)

3. SIMPLIFY to solve for the side length

• Divide both sides by 4:
  • \(\mathrm{s = 144 \div 4}\)
  • \(\mathrm{s = 36}\)

Answer: 36

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students might confuse the relationship between perimeter and side length, thinking that if the perimeter is 144, then one side must also be 144.

This happens when they don't properly connect that "perimeter" means the distance around the entire shape, not just one side. They might set up the equation as \(\mathrm{s = 144}\) instead of \(\mathrm{4s = 144}\).

This leads to confusion and an incorrect answer that's far too large.

The Bottom Line:

This problem requires students to clearly understand what "perimeter" means for a square and translate that understanding into the correct mathematical equation. The actual calculation is straightforward once the right equation is established.