Question

The perimeter of a rectangle is 100m . If a length is decreased by 2 m and the breadth is increased by 3m , the area increases by 44m².Find the length and breadth.

Answer 1

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Here's your answer

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Perimeter = 100

=>2 [ length + breadth ]=100

length + breadth = 100 / 2

length + breadth = 50

Let length be x m .

Breadth = ( 50 - x ) m

Area = x ( 50 - x ) m²

Now , new length = ( x - 2 ) m

And new breadth = ( 50 - x ) + 3

=> ( 53 - x ) m

New Area = ( x - 2 ) ( 53 - x ) m²

As per the condition ,

=>( x - 2 ) ( 53 - x ) - x ( 50 - x ) = 44

=>53 x - x² - 106 + 2 x - 50 x² = 44

=>5 x - 106 = 44

=>5 x = 106 + 44 = 150

=>x = 150 / 5

=>x = 30

Hence ,

The required length = 30 m

And breadth = 50 - 30

=> 20 m

Answer 2

Answer:

$\huge\mathcal{Solution} \:$

Let the length of the given rectangle be x m.

: . Perimeter of the given rectangle = 100 m

: . Perimeter = 2(length + breadth)

100 = 2(x + breadth)

⇒ x + breadth = 50

or Breadth = (50 - x) m

Area of the given rectangle = length × breadth

= x ( 50 - x ) m²

New length = ( x - 2)m

New breadth = ( 50 - x + 3 ) m

= ( 53 - x ) m

:. The area of the given new rectangle =

( x-2) ( 53 - x ) m²

According to the given condition,

Area of new rectangle - Area of given rectangle = 44

i.e ( x - 2 ) ( 53 - x ) ( 50 - x ) = 44

or 53x - x² - 106 + 2x - 50x + x² = 44

or 5x - 106 = 44

or 5x = 44 + 106

i.e 5x = 150

$or \: \: x = \frac{150}{5} = 30$

:. The length of the given rectangle = 30 m

and , the breadth of the given rectangle = ( 50 - 30 ) m

= 20 m

Step-by-step explanation:

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