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 of the given rectangle, $P=2(x+y)$ [$\because$ Perimeter of rectangle $=2(length+breadth)$]

Again, New length $=2x$

New breadth $=2y$

$\therefore$ New perimeter, $P^{\prime }=2(2x+2y)$

$=4(x+y)=2\times 2(x+y)=2P$

$\therefore \frac{P}{P^{\prime }}=\frac{1}{2}$

i.e. $P:P^{\prime }=1:2$

Ratio of perimeters of the original rectangle and the resulting rectangle $=1:2$

(ii) Area of the given rectangle, $A=xy$ [$\because$ Area of rectangle $=(length\times breadth)$]

New Area, $A^{\prime }=\left(2x\right)\left(2y\right)=4\times xy=4A$

$\therefore \frac{A}{A^{\prime }}=\frac{1}{4}$

i.e. $A:A^{\prime }=1:4$

Hence, the ratio of area of the original rectangle and the resulting rectangle $=1:4$