A rectangular paper of 20 cm × 8 cm is folded 3 times. Each fold is made along the
line of symmetry, which is perpendicular to its long edge. The perimeter of the final
folded sheet (in cm) is
Options:
(A) 18
(B) 24
(C) 20
(D) 21
Official Answer Key:
A
Step-by-Step Solution & Explanation
### **Official Solution & Concept Analysis (GATE BT 2024 Q.9)**
**1. Governing Concept**:
- **Topic**: Spatial Aptitude & Paper Folding Symmetry
- Initial paper dimensions: $20\text{ cm} \times 8\text{ cm}$.
- Folded 3 times along the line of symmetry perpendicular to the longer side:
- Fold 1: Longer side 20 cm becomes $10\text{ cm}$; dimensions $10 \times 8$.
- Fold 2: Longer side 10 cm becomes $5\text{ cm}$; dimensions $8 \times 5$.
- Fold 3: Longer side 8 cm becomes $4\text{ cm}$; dimensions $5 \times 4$.
- Perimeter of the final folded rectangle:
$\text{Perimeter} = 2(5 + 4) = 18\text{ cm}$
**2. Option Analysis**:
- **Option (A) [18] is CORRECT**: Matches $2(5 + 4) = 18\text{ cm}$.
- **Option (B) [24] is INCORRECT**: Arises if folding only twice ($2(8 + 4) = 24$ or $2(10 + 2)$).
- **Option (C) [20] is INCORRECT**: Miscalculating fold sequence.
- **Option (D) [21] is INCORRECT**: Arithmetic error.
**3. Final Answer**:
- **Correct Choice**: **A**
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