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Poster on a sheet of given area with given margins: sheet size for the largest printed space

The same question, asked 3 times: 9 May 2023 S2*, 12 May 2024 S2*, 14 May 2026 S2. Every wording below, oldest first.

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  1. Question 1

    9 May 2023 S2

    123
    A poster is to be printed on a rectangular sheet of paper of area 8 m2^2. The margins at the top and bottom of 75 cm each and at the sides 50 cm each are to be left. Then the dimensions i.e. height and breadth of the sheet so that the space available for printing is maximum, are respectively.

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  2. Question 2

    12 May 2024 S2

    109
    A poster is to be printed on a rectangular sheet of paper of area 1818 m2\text{m}^2. The margins at the top and bottom of 75 cm each and at the sides 50 cm each are to be left. Then the dimensions i.e. height and breadth of the sheet, so that the space available for printing is maximum, are respectively

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  3. Question 3

    14 May 2026 S2

    76
    A rectangular sheet of paper has its area 3232 meters2\text{meters}^2. The margins at the top and bottom are 5050 cm each and at the sides 2525 cm each. If the area of the printed space is maximum, then the dimensions of the paper are

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