Question

the perimeter of a rectangle is 240 CM if its length is decreased by 10% and its breadth is increased by 20% we get the same perimeter find the length and breadth of the rectangle

Answer 1

Here’s the answer. It’s just that for second case the new length will be 9x/10 & breadth be 12x/10 but perimeter will be same . After finding the equations just need to solve the equations .

Answer 2

$\huge\fbox{\underline\purple{Answer}:-}$

• Given Perimeter = 240

$\fbox\green{Perimeter = 2( Length+Breadth )}$

$i.e.,2( l+b )$= 240

$:⟹ l+b = 120cm$

Let lenght of Rectangle be ϰ cm .

Then , breadth of the Rectangle = ( 120 - ϰ ) cm

The length is decreased by 10% ,

so new length is

:⟹$x - x \times \frac{10}{100} = x - \frac{x}{10} = \frac{9x}{10}cm.$

Breadth is increased by 20% ,

so new breadth is

:⟹$(120 - x) + (120 - x) \times \frac{20}{100} = (120 - x ) + (120 - x) \times \frac{1}{5}$

:⟹$\frac{5(120 - x) + (120 - x)}{5}$

:⟹$\frac{600 - 5x + 120 - x}{5}$

:⟹$\frac{720 - 6x}{5}cm$

$\boxed{Short~Cut \\ \:Length = \frac{99}{100}x Breadth = \frac{120}{100} (120 - x) \\ \:Perimeter = 2(length + breadth)}$

By the condition , perimeter remains the same,

$i.e.,240cm$

So,

$2( \frac{9x}{10} + \frac{720 - 6x}{5}) = 240$

:⟹ $\frac{9x}{10} \frac{720 - 6x}{5} = 120$

:⟹ $9x + 1440 - 12x = 120 \times 10$

:⟹$1440 - 3x = 1200$

:⟹$- 3x = 1200 - 1440$

:⟹$- 3x = - 240$

:⟹$x = \frac{ - 240}{ - 3} = 80$

.•. Length of the Rectangle = ϰ = 80cm

⠀⠀⠀⠀ ⠀⠀And

.•. Breadth = 120 - ϰ = 120 - 80 = 40cm.