Question

the perimeter of a rectangle is hundred metre is the length is decreased by 2 and the breadth is increased by 3 the area increased by 42 to the power square find the length and breadth of rectangle​

Answer 1

Step-by-step explanation:

Perimeter = 100

=>2 [length + breadth ]=100

length + breadth = 100 / 2

length + breadth = 50

Let length bex m.

Breadth = (50-x) m

Area = x (50 - x) m²

Now, new length = (x - 2) m53

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 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

HOPE IT HELPS YOU!!!!!

Answer 2

Answer:

let the length of the given rectangle be X m.

perimeter of rectangle is hundred metre.

perimeter = 2(length + breadth)

100 = 2(x + breadth)

=> x + breadth = 50

breadth = (50 - x)m

area of the given rectangle is length in to breadth.

= x(50-x)m²

new length = ( x - 2 )

new breadth = ( 50 - x + 3 )m

= (53-x)m

the area of the new rectangle is (x - 2) (53 - x)m²

according to the given condition,

area of new rectangle - area of the given rectangle = 44.

i.e. (x-2) (53-x) - 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 = 150/5 = 30

the length of the given rectangle is 30 m.

and the breadth of the given rectangle is (50-30)

= 20 m.

$\huge\mathfrak{verification}$

area of the given rectangle = (30 × 20)m².

= 600m²

new length = (30-2)m = 28m

new breadth = (20+3)m = 23m

area of new rectangle = (28×23)m² = 644m²

(644-600)m²

= 44m² (which is the same as given)

$\fbox\red{hence , the solution verified}$