Question

The perimeter of a rectangle is 240 centimeter. If its length is increased by 10%and breadth is decreased by 20%,we get the same perimeter. Find the length and breadth of the rectangle.

Answer 1

Given :-

perimeter of rectangle = 240cm

Let l be the length of rectangle and b will be the breadth of rectangle

$= l + b = \frac{240}{2} \\ = l + b = 120$

Let L be the decreased length and B the increased breadth,

Given that length is decreased by 10%

Thus, decrease in length =

$= \frac{10}{100} \times l = \frac{1}{10} \\ = l = \frac{1}{10} = \frac{10l - 1}{10} = \frac{9l}{10}$

Given that the Breadth is increased by 20%

Thus, increase in length =

$\frac{20}{100} \times b = \frac{b}{5} \\ therefore \: b = \frac{b}{5} = \frac{5b + b}{5} = \frac{6b}{5}$

The perimeter of new rectangle is =

$2( \frac{9l}{10} + \frac{6b}{5} ) = 240$

Given that the perimeter of new rectangle = 120

$= 2( \frac{9l}{10} + \frac{6b}{5} ) = 240 \\ \\ = \frac{9l}{10} + \frac{6b}{5} = 120 \\ \\ = \frac{9l}{10} + \frac{12b}{10} = 120 \\ \\ = \frac{9l + 12b}{10} = 120$

= 9l + 12b = 1200

= multiply equation by 9 and subtracting from we have,

= 3b = 120

= b= 40cm

= l = 120 - 40 = 80cm

Thus, the original dimensions of a rectangle are 80cm and 40cm.

I hope this may help you