GATE CS 2024 Set 1 Q9 — General Aptitude

Let us track the dimensions of the rectangular sheet after each fold. Initially, the dimensions are $20\text{ cm} \times 8\text{ cm}$.

1. Initial State:
   • Dimensions: $20\text{ cm} \times 8\text{ cm}$
   • The long edge is $20\text{ cm}$.
2. First Fold:
   • The fold is made perpendicular to the long edge ($20\text{ cm}$), halving it.
   • New dimensions: $\frac{20}{2}\text{ cm} \times 8\text{ cm} = 10\text{ cm} \times 8\text{ cm}$
   • The long edge is now $10\text{ cm}$.
3. Second Fold:
   • The fold is made perpendicular to the current long edge ($10\text{ cm}$), halving it.
   • New dimensions: $\frac{10}{2}\text{ cm} \times 8\text{ cm} = 5\text{ cm} \times 8\text{ cm}$
   • The long edge is now $8\text{ cm}$.
4. Third Fold:
   • The fold is made perpendicular to the current long edge ($8\text{ cm}$), halving it.
   • New dimensions: $5\text{ cm} \times \frac{8}{2}\text{ cm} = 5\text{ cm} \times 4\text{ cm}$

The final folded sheet has dimensions $5\text{ cm} \times 4\text{ cm}$.

The perimeter of this final sheet is calculated as: $$\text{Perimeter} = 2 \times (\text{length} + \text{width}) = 2 \times (5 + 4) = 18\text{ cm}$$

Thus, the correct option is A.