Question

The perimeter of a rectangle is 240 cm . If it's length is increased by 10percent and its breadth is decreased by 20 percent then we get the same perimeter find the length and breadth of the rectangle

Answer 1

Let the length be x and breadth be y

We know that perimeter = 2(l + b) = 240

=> 2(x + y) = 240

=> (x + y) = 240/2 cm

=> x + y = 120

Now given if length is increased by 10% and breadth is decreased by 20% then perimeter remains the same

So,

length is increased by 10%

=>
$x + \frac{10}{100} \times x \\ \\ = > x + \frac{x}{10} \\ \\ = > \frac{10x}{10} + \frac{x}{10} \\ \\ = \frac{11x}{10}$


So new length = 11x/10

Now breadth is decreased by 20%

$= > y - \frac{20}{100} \times y \\ \\ = > y - \frac{y}{5} \\ \\ = > \frac{5y}{5} - \frac{y}{5} \\ \\ = > \frac{4y}{5}$


Now perimeter is same

=>
$2( \frac{11x}{10} + \frac{4y}{5} ) = 240$

$= > \frac{11x}{10} + \frac{4y}{5} = \frac{240}{2} \\ \\ = > \frac{11x}{10} + \frac{4y}{5} = 120$

but, we know that,

x + y = 120cm

=>
$\frac{11x}{10} + \frac{4y}{5} = x + y \\ \\ = > \frac{11x}{10} - x = y - \frac{4y}{5} \\ \\ = > \frac{11x}{10} - \frac{10x}{10} = \frac{5y}{5} - \frac{4y}{5} \\ \\ = > \frac{x}{10} = \frac{y}{5} \\ \\ = > 5x = 10y \\ \\ = > x = \frac{10y}{5} \\ \\ = > x = 2y$


Now, x + y = 120

but x = 2y

=> 2y + y = 120

=> 3y = 120

=> y = 120/3

=> y = 40 cm

Now x = 2y

=> x = 2(40)

=> x = 80cm


Length = x = 80cm
Breadth = y = 40cm


Hope it helps dear friend ☺️✌️