Q7 of 38 Page 5

I cut three square shaped paper and notice the changes in areas

If - a. Length becomes double.


b. Length becomes half.


Given that,

We have three square shaped paper.


Let side of the square shaped paper be x unit.


That is,


Side = x unit


Area of square is given by,


Area = (Side)2


So,


Area of one square paper is given as,


Area = (x)2


⇒ Area = x2 …(i)


(a). According to the question,


Original dimensions:


Length = x


Breadth = x


New dimensions:


Length’ = 2 × Length


⇒ Length’ = 2x


New Area = (Length’)2


⇒ New Area = (2x)2


⇒ New Area = 4x2 …(ii)


Then, change in area is given by



[from equation (i) and (ii), New area = 4x2 and Original area = x2]



Hence, the new area is 4 times the original area of the square-shaped paper.


(b) According to the question,


Original dimensions:


Length = x


Breadth = x


New dimensions:




Breadth’ = x


New Area = Length’ × Breadth’



…(iii)


Then, change in area is given by



[from equation (i) and (iii), and original area = x2]



Hence, new area is half of the original area of the square-shaped paper.


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