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Sum

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

Concept: Perimeter of a Rectangle

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