The perimeter of rectangle PQRS is 26 inches. The length of the rectangle is 9 inches. What is the width,...
GMAT Geometry & Trigonometry : (Geo_Trig) Questions
The perimeter of rectangle \(\mathrm{PQRS}\) is \(\mathrm{26}\) inches. The length of the rectangle is \(\mathrm{9}\) inches. What is the width, in inches, of the rectangle?
1. TRANSLATE the problem information
- Given information:
- Perimeter = 26 inches
- Length = 9 inches
- Need to find: width
This translates to the equation: \(\mathrm{26 = 2(9 + width)}\)
2. SIMPLIFY to solve for width
- Start with: \(\mathrm{26 = 2(9 + width)}\)
- Distribute the 2: \(\mathrm{26 = 18 + 2(width)}\)
- Subtract 18 from both sides: \(\mathrm{8 = 2(width)}\)
- Divide both sides by 2: \(\mathrm{width = 4\text{ inches}}\)
Answer: A (4)
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak SIMPLIFY execution: Students correctly set up \(\mathrm{26 = 2(9 + width)}\) and get to \(\mathrm{8 = 2(width)}\), but then forget the final division step.
They stop at \(\mathrm{8 = 2(width)}\) and think the width is 8, leading them to select Choice B (8).
Second Most Common Error:
Poor TRANSLATE reasoning: Students misunderstand what the perimeter formula represents and think width = perimeter - length.
They calculate \(\mathrm{26 - 9 = 17}\) and select Choice E (17), not realizing that perimeter accounts for both pairs of opposite sides.
The Bottom Line:
This problem tests whether students truly understand that rectangle perimeter involves adding BOTH the length AND width TWICE, not just once each. The algebraic manipulation is straightforward, but the setup requires careful translation of the geometric relationship.