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.

Answer 1

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