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Answers
Step-by-step explanation:
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
Change in area new area/ original area
change in area = 4x²/ x²
[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:
Length = Length
--------------
2
Length. = x
-----
2
Breadth’ = x
New Area = Length’ × Breadth’
New area =. x
--- x x
2
New area = x² …(iii)
----
2
Then, change in area is given by
Change in area = (x²)
-----
x²
[from equation (i) and (iii),
New area = x²
----
2
and original area = x²]
Change in area = 1\ 2
Hence, new area is half of the original area of the square-shaped paper.