Question:A rectangular banner has a length of 33 centimeters and a width that is 2 centimeters less than its length....
GMAT Geometry & Trigonometry : (Geo_Trig) Questions
A rectangular banner has a length of \(\mathrm{33}\) centimeters and a width that is \(\mathrm{2}\) centimeters less than its length. What is the area, in square centimeters, of the banner?
Enter your answer as an integer (units not required).
1. TRANSLATE the problem information
- Given information:
- Length = 33 centimeters
- Width is "2 centimeters less than its length"
- What this tells us: \(\mathrm{Width = Length - 2 = 33 - 2 = 31}\) centimeters
2. INFER what we need to find the area
- To find the area of a rectangle, we need both the length and width
- We have the length (33 cm) and can calculate the width (31 cm)
- We can now apply the area formula
3. SIMPLIFY by applying the area formula and calculating
- \(\mathrm{Area = Length \times Width = 33 \times 31}\)
- Calculate: \(\mathrm{33 \times 31 = 1023}\) square centimeters
Answer: 1023
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak TRANSLATE skill: Misinterpreting "2 centimeters less than its length"
Students might think this means \(\mathrm{Width = Length + 2 = 33 + 2 = 35}\), leading them to calculate \(\mathrm{Area = 33 \times 35 = 1155}\). This leads to confusion since 1155 won't match any reasonable expectation for the problem.
Second Most Common Error:
Poor SIMPLIFY execution: Making arithmetic errors when calculating \(\mathrm{33 \times 31}\)
Students might rush through the multiplication and get values like 1033 or 1013, leading to incorrect final answers that seem plausible but are wrong.
The Bottom Line:
This problem tests students' ability to carefully translate verbal relationships into mathematical expressions. The phrase "2 less than" is a key linguistic cue that requires precise mathematical translation before any calculations can begin.