Question

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:

• A. 14:11
• B. 11:14
• C. 18:11
• D. 11:18

Hint:

For folding problems, carefully follow each step to update dimensions after every fold. Always double-check ratios to ensure they align with the question's requirements.

Answer 1

The Correct Option is A

Step 1: first Fold sheet A twice using FO1.
In FO1, the sheet is folded along the longer edge. After the first fold, the dimensions of sheet A are: \[ \frac{24}{2} \, {cm} \times 16 \, {cm} = 12 \, {cm} \times 16 \, {cm}. \] After the second fold along the longer edge, the dimensions become: \[ \frac{12}{2} \, {cm} \times 16 \, {cm} = 6 \, {cm} \times 16 \, {cm}. \] The perimeter of the final folded shape of A is: \[ 2 \times (6 + 16) = 2 \times 22 = 44 \, {cm}. \] Step 2: Fold sheet B twice using FO2.
In FO2, the sheet is folded along the shorter edge. After the first fold, the dimensions of sheet B are: \[ 24 \, {cm} \times \frac{16}{2} \, {cm} = 24 \, {cm} \times 8 \, {cm}. \] After the second fold along the shorter edge, the dimensions become: \[ 24 \, {cm} \times \frac{8}{2} \, {cm} = 24 \, {cm} \times 4 \, {cm}. \] The perimeter of the final folded shape of B is: \[ 2 \times (24 + 4) = 2 \times 28 = 56 \, {cm}. \] Step 3: Compute the ratio of perimeters.
The ratio of the perimeters of A to B is: \[ \frac{44}{56} = \frac{11}{14}. \] Since the question asks for the inverse ratio (final to initial), the ratio is: \[ {Ratio} = 14:11. \] Final Answer: \[ \boxed{{(1) 14:11}} \]