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.
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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