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Question
Each side of a rectangle is doubled. Find the ratio between :
(i) perimeters of the original rectangle and the resulting rectangle.
(ii) areas of the original rectangle and the resulting rectangle.
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Solution
Let length of the rectangle = x
and breadth of the rectangle = y
(i)
Perimeter P = 2(x + y)
Again, new length = 2x
New breadth = 2y
∴ New perimeter P' = 2(2x + 2y)
= 4(x + y) = 2.2(x + y) = 2P
= `"P"/("P"') = 1/2` i.e. P : P' = 1 : 2
(ii)
Area A = xy
New Area A' = (2x)(2y) = 4xy = 4A
∴ `"A"/("A"') = 1/4` i.e. A : A' = 1 : 4
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