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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

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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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2021-07-31T04:16:39+00:00
2021-07-31T04:16:39+00:00 1 Answers
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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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