Two identical sheets A and B, of dimensions 24 cm x 16 cm, can be folded into half using two distinct operations, FO1 or...

Question

Two identical sheets A and B, of dimensions 24 cm x 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

Accepted Answer

The ratio of the perimeters of sheets A and B is 14 : 11. Both sheets start as 24 cm x 16 cm rectangles. Folding operation FO1 folds parallel to the long edge, which means the fold axis runs along the 24 cm direction, halving the 16 cm width. FO2 folds parallel to the short edge, meaning the fold axis runs along the 16 cm direction, halving the 24 cm length. Sheet A is folded twice with FO1 (width is halved twice), and sheet B is folded twice with FO2 (length is halved twice). We then compare their perimeters.