GATE CS 2024 Set 1 — Question 9

The initial dimensions of the paper are $20 \text{ cm} \times 8 \text{ cm}$.Fold 1:
The fold is made along the line of symmetry perpendicular to the long edge ($20 \text{ cm}$). This halves the length.
New dimensions: $\frac{20}{2} \times 8 = 10 \text{ cm} \times 8 \text{ cm}$.Fold 2:
The current dimensions are $10 \text{ cm} \times 8 \text{ cm}$. The long edge is $10 \text{ cm}$. The fold is perpendicular to this edge.
New dimensions: $\frac{10}{2} \times 8 = 5 \text{ cm} \times 8 \text{ cm}$.Fold 3:
The current dimensions are $5 \text{ cm} \times 8 \text{ cm}$. The long edge is now $8 \text{ cm}$ (since $8 > 5$). The fold is perpendicular to the $8 \text{ cm}$ edge.
New dimensions: $5 \text{ cm} \times \frac{8}{2} = 5 \text{ cm} \times 4 \text{ cm}$.The final folded sheet is a rectangle of size $5 \text{ cm} \times 4 \text{ cm}$.
The perimeter $P$ is given by:$$P = 2 \times (\text{length} + \text{width})$$$$P = 2 \times (5 + 4) = 2 \times 9 = 18 \text{ cm}$$