Question

the perimeter of a rectangle is 100 m. if the length is decreased by 2m and the breadth is increased by 3m, then, area increased by 44m^2. find the length and breadth of the rectangle. I want step by step answer. But the ans is 30m, 20m. Ans will be marked as brainliest if it is nice.

Answer 1

Let 'l' be the length and 'b' be the breadth of the rectangle.

Perimeter = 100m

=> 2(l+b) = 100m

=> l + b = 100m / 2

=> l + b + 50m...............1

Area = l × b

Acc. to the ques.

=> (l - 2) (b + 3) = area + 44

=> (l - 2) (b + 3) = lb + 44

=> l ( b + 3) - 2( b + 3) = lb + 44

=> lb + 3l - 2b - 6 = lb + 44

=> lb + 3l - 2b = lb + 44 + 6

=> 3l - 2b = lb + 50.............2

Eq 1 ----------> l + b = 50 ( Multiply the whole eq. by 2)

Eq formed will be -----------> 2l + 2b = 100......( Let this be eq 3)

Eq 2 ----------> 3l - 2b = lb + 50

By adding eq 2 and 3

=> 5l = 150

=> l = 150/5

=> l = 30

The length of the rectangle is 30m.

l + b = 50 m

30m + b = 50m

b = 20m

The breadth of the rectangle is 20m.

Ans. = The length of the given rectangle is 30m and its breadth is 20m.

Hope it helps!!!
 

Answer 2

GIVEN :

• The perimeter of the rectangle = 100 m.

• If here the length is decreased by 2m and then the Breadth is increased by 3m.

• Then after increasing Length and Breadth we got here area = 44cm²

TO FIND :

• The Length and Breadth of the rectangle= ?

STEP - BY - STEP EXPLAINATION :

→ Perimeter 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 - x )m

→ 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 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) - x (50- x) = 44

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

or 5x - 106 = 44

or 5x = 44 + 106

i.e. 5x = 150

$= > x = \frac{150}{5} = 30$

The length of the Given rectangle = 30 m

and

The Breadth of the Given rectangle = ?

Now,

=> (50 - 30)m

=> 20m

Therefore, the length = 30m and Breadth = 20m.