Question:A regular hexagon has perimeter P (in centimeters) given by P = 6s, where s is the side length in...
GMAT Algebra : (Alg) Questions
- A regular hexagon has perimeter \(\mathrm{P}\) (in centimeters) given by \(\mathrm{P = 6s}\), where \(\mathrm{s}\) is the side length in centimeters.
- If the perimeter is \(66\) centimeters,
- What is the value of \(\mathrm{s}\)?
Answer Format: Enter your answer as an integer. Do not include units.
1. TRANSLATE the problem information
- Given information:
- Regular hexagon perimeter formula: \(\mathrm{P = 6s}\)
- Actual perimeter: \(\mathrm{P = 66}\) centimeters
- Need to find: side length s
2. TRANSLATE to set up the equation
- Since \(\mathrm{P = 66}\) and \(\mathrm{P = 6s}\), we can substitute:
\(\mathrm{66 = 6s}\) - This gives us a simple linear equation to solve
3. SIMPLIFY by solving for s
- Divide both sides by 6:
\(\mathrm{s = 66 ÷ 6 = 11}\) - Check: \(\mathrm{6 × 11 = 66}\) ✓
Answer: 11
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak TRANSLATE skill: Students may not recognize that they need to substitute \(\mathrm{P = 66}\) into the given formula \(\mathrm{P = 6s}\). Instead, they might try to work with the formula in abstract terms or get confused about what to do with the given perimeter value.
This leads to confusion and guessing rather than systematic problem-solving.
Second Most Common Error:
Poor SIMPLIFY execution: Students correctly set up \(\mathrm{66 = 6s}\) but make arithmetic errors when dividing 66 by 6. Common mistakes include getting 10 (thinking 60 ÷ 6) or 12 (misremembering division facts).
This may lead them to select incorrect numerical answers if multiple choice options are available.
The Bottom Line:
This problem tests whether students can connect geometric formulas to algebraic equation-solving. The key insight is recognizing that geometric problems often reduce to simple algebra once the relationships are properly translated into mathematical equations.