Two identical sheets A and B, of dimensions $24$ cm $\times$ $16$ cm, can be folded into half using two distinct operations, FO1 or FO2.
In FO1, the axis of folding remains parallel to the initial long edge, and in FO2, the axis of folding remains parallel to the initial short edge.
If sheet A is folded twice using FO1, and sheet B is folded twice using FO2, the ratio of the perimeters of the final shapes of A and B is
We need to determine the ratio of the perimeters of two identical sheets, A and B, after specific folding operations.
Initial Sheet Dimensions
Both sheets A and B have initial dimensions: Length ($L_0$) = $24$ cm and Width ($W_0$) = $16$ cm.
Sheet A Folding Analysis (FO1)
Operation FO1 involves folding with the axis parallel to the initial long edge ($24$ cm). This means the width dimension is halved in each fold.
- After 1st fold (FO1): The length remains $24$ cm, and the width becomes $\frac{16}{2} = 8$ cm. Dimensions are $24$ cm $\times$ $8$ cm.
- After 2nd fold (FO1): The length remains $24$ cm, and the width becomes $\frac{8}{2} = 4$ cm. Final dimensions are $24$ cm $\times$ $4$ cm.
The perimeter of the final shape of Sheet A ($P_A$) is calculated using the formula $P = 2 \times (length + width)$.
$P_A = 2 \times (24 \text{ cm} + 4 \text{ cm}) = 2 \times 28 \text{ cm} = 56 \text{ cm}$
Sheet B Folding Analysis (FO2)
Operation FO2 involves folding with the axis parallel to the initial short edge ($16$ cm). This means the length dimension is halved in each fold.
- After 1st fold (FO2): The width remains $16$ cm, and the length becomes $\frac{24}{2} = 12$ cm. Dimensions are $12$ cm $\times$ $16$ cm.
- After 2nd fold (FO2): The width remains $16$ cm, and the length becomes $\frac{12}{2} = 6$ cm. Final dimensions are $6$ cm $\times$ $16$ cm.
The perimeter of the final shape of Sheet B ($P_B$) is:
$P_B = 2 \times (6 \text{ cm} + 16 \text{ cm}) = 2 \times 22 \text{ cm} = 44 \text{ cm}$
Ratio Calculation
The ratio of the perimeters of the final shapes of A and B is $P_A : P_B$.
$ \frac{P_A}{P_B} = \frac{56 \text{ cm}}{44 \text{ cm}} $
To simplify the ratio, we find the greatest common divisor of 56 and 44, which is 4.
$ \frac{56 \div 4}{44 \div 4} = \frac{14}{11} $
The ratio is $14:11$.
Important Questions from Paper Folding
The paper as shown in the figure is folded to make a cube where each square corresponds to a particular face of the cube. Which one of the following options correctly represents the cube?
Note: The figures shown are representative.
A planar rectangular paper has two V-shaped pieces attached as shown below.
This piece of paper is folded to make the following closed three-dimensional object.
The number of folds required to form the above object is
Consider a cube made by folding a single sheet of paper of appropriate shape.
The interior faces of the cube are all blank. However, the exterior faces that arenot visible in the above view may not be blank.
Which one of the following represents a possible unfolding of the cube?- Consider two rectangular sheets, Sheet M and Sheet N of dimensions 6 cm x 4 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 M three times.
Folding operation 2 is carried out on Sheet N three times.
The ratio of perimeters of the final folded shape of Sheet N to the final folded shape of Sheet M is ________. 
A transparent square sheet shown above is folded along the dotted line. The folded sheet will look like ________________.
