The perimeter of triangle ABC is 17 inches, the length of side AB is 4 inches, and the length of...

1. TRANSLATE the problem information

• Given information:
  • Perimeter of triangle ABC = 17 inches
  • Side AB = 4 inches
  • Side AC = 7 inches
  • Unknown: Side BC

• What this tells us: We can use the perimeter formula to set up an equation

2. TRANSLATE the perimeter definition into an equation

• Since perimeter equals the sum of all three sides:
  \(\mathrm{AB + AC + BC = Perimeter}\)
  \(\mathrm{4 + 7 + BC = 17}\)

3. SIMPLIFY to solve for the unknown side

• Combine the known sides: \(\mathrm{4 + 7 = 11}\)
• So our equation becomes: \(\mathrm{11 + BC = 17}\)
• Subtract 11 from both sides: \(\mathrm{BC = 17 - 11 = 6}\)

Answer: B. 6

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE reasoning: Students recognize they need to find the third side but don't properly set up the equation. Instead, they might add the two known sides together.

They calculate: \(\mathrm{AB + AC = 4 + 7 = 11}\)

This may lead them to select Choice D (11) without recognizing that this represents the sum of two sides, not the third side.

Second Most Common Error:

Poor attention to detail: Students see the values 4 and 7 in the problem and in the answer choices, then select one of these without doing any calculations.

This causes them to select Choice A (4) or Choice C (7) by assuming the unknown side equals one of the known sides.

The Bottom Line:

This problem tests whether students understand that perimeter problems require setting up and solving an equation, not just manipulating the given numbers. The key insight is translating "perimeter equals sum of all sides" into mathematical form.