Question

the perimeter of a rectangle is 240 metres it is length is decreased by 10% and breadth is increased by 20% we get the same perimeter find the length and the breadth of the both the rectangles.​

Answer 1

L=10/100×240

=24

B=20/100×24

=48

Answer 2

Let the Length of the Original Rectangle be : L

Let the Breadth of the Original Rectangle be : B

Given : Perimeter of the Rectangle is 240 meters

★  We know that : Perimeter of a Rectangle is 2[Length + Breadth]

$:\implies$  2[L + B] = 240

$:\implies$  L + B = 120

$:\implies$  L = 120 - B

Given : Length is decreased by 10%

$:\implies$ Length of the New Rectangle = L - 10% × [L]

$:\implies \mathsf{Length\;of\;the\;New\;Rectangle = \bigg[L - \dfrac{10}{100} \times L\bigg]}$

$:\implies \mathsf{Length\;of\;the\;New\;Rectangle = \bigg[L - \dfrac{L}{10}\bigg]}$

$:\implies \mathsf{Length\;of\;the\;New\;Rectangle = \dfrac{9L}{10}}$

Given : Breadth is increased by 20%

$:\implies$ Breadth of the New Rectangle = B + 20% × [B]

$:\implies \mathsf{Breadth\;of\;the\;New\;Rectangle = \bigg[B + \dfrac{20}{100} \times B\bigg]}$

$:\implies \mathsf{Breadth\;of\;the\;New\;Rectangle = \bigg[B + \dfrac{B}{5}\bigg]}$

$:\implies \mathsf{Breadth\;of\;the\;New\;Rectangle = \dfrac{6B}{5}}$

Given : After the Decreasing of Length and Increasing of Breadth, The Perimeter of the New Rectangle still remains the same.

$:\implies \mathsf{2\bigg[\dfrac{9L}{10} + \dfrac{6B}{5}\bigg] = 240}$

$:\implies \mathsf{\bigg[\dfrac{9L}{10} + \dfrac{6B}{5}\bigg] = 120}$

$:\implies \mathsf{\dfrac{9L + 12B}{10} = 120}$

$:\implies \mathsf{\dfrac{3L + 4B}{10} = 40}$

$:\implies \mathsf{3L + 4B = 400}$

Substituting the value of L in the above Equation, We get :

$\mathsf{:\implies 3(120 - B) + 4B = 400}$

$\mathsf{:\implies 360 - 3B + 4B = 400}$

$\mathsf{:\implies B = 400 - 360}$

$\mathsf{:\implies B = 40}$

$:\implies$  Breadth of the Original Rectangle = 40 meters

Substituting the Value of B in Equation L = 120 - B, We get :

$\mathsf{:\implies L = 120 - 40}$

$\mathsf{:\implies L = 80}$

$:\implies$  Length of the Original Rectangle = 80 meters

$:\implies \mathsf{Length\;of\;New\;Rectangle = \dfrac{9L}{10} = \bigg(\dfrac{9 \times 80}{10}\bigg) = 72\;m}$

$:\implies \mathsf{Breadth\;of\;New\;Rectangle = \dfrac{6B}{5} = \bigg(\dfrac{6 \times 40}{5}\bigg) = 48\;m}$