Discussion
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 ______.
Answer: A
The ratio is 13 : 7.
Joining the short edges halves the long side; joining the long edges halves the short side. Track each sheet, starting from 6 cm by 4 cm:
- Sheet M, operation 1 three times: 6 x 4, then 3 x 4, then 3 x 2, then 1.5 x 2. Each fold halves whichever side is currently longer. Perimeter 2(1.5 + 2) = 7 cm.
- Sheet N, operation 2 three times: 6 x 4, then 6 x 2, then 6 x 1, then 6 x 0.5. The 6 cm side is never folded. Perimeter 2(6 + 0.5) = 13 cm.
So N : M = 13 : 7. The question asks for N first; 7 : 13 would be the ratio the other way round, and none of 3 : 2, 7 : 5 or 5 : 13 matches the two perimeters.
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