Question

the perimeter of a rectangular field is hundred metre if the length of the field is decreased by 2 metre and the breadth is increased by 3 the areas increased by 44 square metre find the length and the breadth of the field



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Answer 1

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 + 2x - 50 x + 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

$\huge\underline\bold\orange{Answer:}$

Let the length of given rectangle be x

$\because$ Perimeter of given rectangle = 100 metre

$\therefore$ Perimeter = 2(l+b)

$\implies$ 100 =2(x+Breadth)

$\implies$ x + breadth = 50 m

Breadth = (50-x) metre

Area of given rectangle= Length × Breadth

$\implies$ x(50-x) m^2

New Length = (x-2) m

New breadth = (50-x+3) m

New Breadth = (53-x) m

$\therefore$ The area of New Rectangle = (x-2)(53-x)m^2

$\textbf{\underline{\underline{According\:To\:Question :}}}$

Area of New Rectangle - Area of given rectangle = 44

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

$53x - {x}^{2} - 106 + 2x - 50x + {x}^{2} = 44$

$5x - 106 = 44$

$5x = 44 + 106$

$5x = 150$

$x = \frac{150}{5}$

$x = 30$

$\therefore$ Length of Given Rectangle= 30 m

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

Thus,

Breadth = 20m