Question:The perimeter of an equilateral triangle is 135. What is the length of each side?154567.5135

1. TRANSLATE the problem information

• Given information:
  • We have an equilateral triangle
  • The perimeter is 135
  • We need to find the length of each side

• What this tells us: Since it's equilateral, all three sides have the same length

2. INFER the mathematical relationship

• In an equilateral triangle, if each side has length \(\mathrm{s}\), then:
  • \(\mathrm{Perimeter = s + s + s = 3s}\)
• Since perimeter = 135, we have: \(\mathrm{3s = 135}\)
• To find one side length, we need to divide the total perimeter by 3

3. SIMPLIFY to find the answer

• Solve the equation: \(\mathrm{s = 135 \div 3 = 45}\)

Answer: B) 45

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE reasoning: Students read "the perimeter is 135" and immediately select 135 as their answer without recognizing that the question asks for the length of each side, not the perimeter itself.

They think: "The problem says the perimeter is 135, so the answer must be 135."

This may lead them to select Choice D (135)

Second Most Common Error:

Conceptual confusion about triangle sides: Students might think a triangle has only 2 sides or get confused about how many sides to divide by.

They perform \(\mathrm{135 \div 2 = 67.5}\) instead of \(\mathrm{135 \div 3 = 45}\).

This may lead them to select Choice C (67.5)

The Bottom Line:

This problem tests whether students can distinguish between being given a total measurement (perimeter) versus finding an individual measurement (side length), and whether they remember that equilateral triangles have three equal sides.