GATE EC 2024 Set 1 — Question 10
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General Aptitude → Quantitative Aptitude → Mensuration & Geometry
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Question
Two identical sheets A and B, of dimensions 24 cm 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
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
Correct answer
(A) 14:11
Solution
Let the initial dimensions of the sheets be length cm and width cm.Sheet A: Folded twice using FO1 (axis parallel to the initial long edge)
FO1 means the folding axis is parallel to the long edge. So, the long edge remains constant, and the short edge is halved with each fold.
Width = cm
Dimensions: 24 cm 8 cm
Width = cm
Dimensions: 24 cm 4 cm The perimeter of the final shape of A is cm.Sheet B: Folded twice using FO2 (axis parallel to the initial short edge)
FO2 means the folding axis is parallel to the short edge. So, the short edge remains constant, and the long edge is halved with each fold.
Width = cm
Dimensions: 12 cm 16 cm
Width = cm
Dimensions: 6 cm 16 cm The perimeter of the final shape of B is cm.Ratio of the perimeters of A and B:
Ratio =
Divide both sides by 4:
Ratio = The final answer is
FO1 means the folding axis is parallel to the long edge. So, the long edge remains constant, and the short edge is halved with each fold.
1.After the first fold (FO1):
Length = cmWidth = cm
Dimensions: 24 cm 8 cm
2.After the second fold (FO1):
Length = cmWidth = cm
Dimensions: 24 cm 4 cm The perimeter of the final shape of A is cm.Sheet B: Folded twice using FO2 (axis parallel to the initial short edge)
FO2 means the folding axis is parallel to the short edge. So, the short edge remains constant, and the long edge is halved with each fold.
1.After the first fold (FO2):
Length = cmWidth = cm
Dimensions: 12 cm 16 cm
2.After the second fold (FO2):
Length = cmWidth = cm
Dimensions: 6 cm 16 cm The perimeter of the final shape of B is cm.Ratio of the perimeters of A and B:
Ratio =
Divide both sides by 4:
Ratio = The final answer is
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