GATE Civil Engineering

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Consider two rectangular sheets, Sheet $\text{M}$ and Sheet $\text{N}$ of dimensions $6\:\text{cm} \times 4\: \text{cm}$ each.

- Folding operation $1:$ The sheet is folded into half by joining the short edges of the current shape.
- Folding operation $2:$ The sheet is folded into half by joining the long edges of the current shape.

Folding operation $1$ is carried out on Sheet $\text{M}$ three times.

Folding operation $2$ is carried out on Sheet $\text{N}$ three times.

The ratio of perimeters of the final folded shape of Sheet $\text{N}$ to the final folded shape of Sheet $\text{M}$ is _____________.

- $13:7$
- $3:2$
- $7:5$
- $5:13$

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Best answer

Sheet $\text{M}$ and sheet $\text{N}$ are of dimensions $6\:\text{cm} \times 4\: \text{cm}$ each.

On Sheets $M$ and $N$, if we perform the given operations, we get as follows.

Now, the perimeter of the final folded shape of sheet $M = 2(1.5+2) = 7\;\text{cm},$ and the perimeter of the final folded shape of sheet $N = 2(0.5+6) = 13\;\text{cm}.$

$\therefore$ The ratio of perimeters of the final folded shape of sheet $N$ to the final folded shape of sheet $M$ is $ = 13:7.$

So, the correct answer is $(A).$

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