Question

The length of the rectangle exceeds it's breadth by 7cm if the length is decreased by 4cm and breadth is increased by 3cm the area of new rectangle is same as the original rectangle.Find the length and breadth of the rectangle

Answer 1

Let the length be "l" and breadth be "b"
Given that,
l = b + 7 
Area initially = l x b = lb
final length = l - 4
and final breadth = b + 3
Area now = (l - 4)(b + 3) = lb + 3l - 4b - 12
Given that the areas are same
So, lb = lb + 3l - 4b -12
     0 = 3l - 4b - 12
     0 = 3(b + 7) - 4b - 12
     0 = 3b + 21 - 4b - 12
     0 = -b + 9
     b = 9 cm
Implies l = 9 + 7 = 16 cm

Answer 2

Solution:-

given:-

• The length of the rectangle exceeds it's breadth by 7cm.

• If the length is decreased by 4cm and the breadth is increased by 3cm.

• The area of new rectangle is the same as the area of original rectangle.

Find:-

• The length and breadth of the original rectangle = ?

Formula:-

=> Area of rectangle

= length(L) × breadth(B)

Now, by given,

let, x be the breadth of rectangle so,

for original rectangle.

• breadth = B1 = x ........ ( 1 )

• length = L1 = x + 7 ........ ( 2 )

so, now....

• for new rectangle

• breadth = B2 = x + 3 ........ (3)

• length = L2 = x + 7 - 4 ....... ( 4 )

we know,

=> (Area of new rectangle) = (Area of oringinal rectangle)

=> L2 × B2 = L1 × B1

=>( x + 7 - 4 ) ( x + 3 ) = ( x + 7) ( x )

=> ( x + 3 ) ( x + 3 ) = x² + 7x

=> ( x + 3 )² = x² + 7x

=> x² + 6x + 9 = x² + 7x

=> x² - x² + 6x - 7x + 9 = 0

=> - x + 9 = 0

=> - x = - 9

=> x = 9

From ( 1 ),

• breadth = x = 9 cm.

From ( 2 ),

• length = x + 7

• length = 9 + 7

• length = 16 cm.

Hence length and breadth of original rectangle is 16cm and 9cm respectively.

i hops it helps you.