Jack and Jill are each given a sheet of paper in the shape of a rectangle.Each of them cut the paper into two equal rectangles.The

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Jack and Jill are each given a sheet of paper in the shape of a rectangle.Each of them cut the paper into two equal rectangles.The perimeters of Jack’s rectangles are 40 cm and Jill’s 50 cm.Find the perimeter and the area of the uncut sheet of paper.​

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Skylar 2 months 2021-07-31T04:16:39+00:00 1 Answers 0 views 0

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    2021-07-31T04:18:07+00:00

    Given : Jack and Jill are each given a sheet of paper in the shape of a rectangle. Each of them cut the paper into two equal rectangles.

    The perimeters of Jack’s rectangles are 40 cm and Jill’s 50 cm.

    To Find : the perimeter and the area of the uncut sheet of paper.​

    Solution:

    Let say original sheet of paper is in size  2a and 2b

    Perimeter = 2 (2a + 2b)  = 4(a + b)

    Area = 2a * 2b = 4ab

    let say  Jack cut it from middle of side 2b hence jack get rectangles

    as with sides  2a  and b

    Perimeter of 1 rectangle = 2 ( 2a + b)  = 4a + 2b

    Perimeter of both rectangles = 2 ( 4a + 2b) = 8a  + 4b

    8a + 4b  = 40

    => 2a + b = 10  Eq1

    d Jill cuts from middle of side 2a  hence Jill gets rectangles

    as with sides  a  and 2b

    Perimeter of 1 rectangle = 2 (  a + 2b)  = 2a + 4b

    Perimeter of both rectangles = 2 ( 2a + 4b) = 4a  + 8b

    4a + 8b  = 50

    => 2a + 4b = 25  Eq2

    Eq2 – Eq1

    => 3b = 15

    => b = 5

    2a + b = 10

    => 2a = 5

    => a = 2.5

    a = 2.5  , b = 5

    Perimeter =  4(a + b)  = 4 ( 2.5 + 5) = 4 ( 7.5)  = 30 cm

    Area =  4ab  = 4 (2.5)(5)  = 50 cm²

    perimeter and the area of the uncut sheet of paper are 30 cm and 50 cm² respectively

    if The perimeters of Jack’s rectangles are 40 cm and Jill’s 50 cm are of one rectangle rather than both

    then  perimeter and the area of the uncut sheet of paper are 60 cm and 200 cm² respectively

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