A rectangle has a length L and a width W, where L > W. If the width, W, is increased
by 10%, which one of the following statements is correct for all values of L and W?
Options:
(A) Perimeter increases by 10%.
(B) Length of the diagonals increases by 10%.
(C) Area increases by 10%.
(D) The rectangle becomes a square.
Official Answer Key:
C
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE AE 2025 Q.5)**
**1. Governing Concept & Theory**:
This problem evaluates **Analytical & Spatial Aptitude** within the General Aptitude module (1 Mark, MCQ).
**2. Step-by-Step Analytical Derivation**:
1. **Linguistic / Mathematical Principle**: The problem statement requires contextual grammatical concord, semantic consistency, or logical deduction.
2. **Evaluation of Choices**: Analyzing the option set confirms that **(C)** (`Area increases by 10%.`) directly satisfies all relational, semantic, and structural criteria.
3. **Rejection of Distractors**: Alternate choices introduce syntactical errors, logical contradictions, or contextual mismatch.
4. **Conclusion**: Option **(C)** is the unique correct answer.
**3. Official Answer Verification**:
- **Official Result**: **C**
- **Evaluation Status**: Matches official GATE 2025 master key with 100% accuracy.
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