Question

the length of a rectangle exceeds with the breadth by 7cm the length of is decreased by 4 cm and the breadth is increased by 3 cm the area of rectangle is the same of the area of the original rectangle find the length and the breadth of the rectangle ​

Answer 1

Step-by-step explanation:

Let the breadth of rectangle be x.

Then, length = x + 7

Original Area of rectangle with sides x and x + 7 = x(x+7)

= x² + 7x

If length is decreased by 4cm, then new length = x + 7 - 4 = x + 3

If breadth is increased by 3 cm, then new breadth = x + 3

New Area of rectangle = (x+3)(x+3)

= (x+3)²

= x² + 9 + 6x

Given, Original Area = New Area

x² + 7x = x² + 9 + 6x

= 7x - 6x = 9

= x = 9

Breadth of Rectangle = x

= 9cm

Length of Rectangle = x + 7

= 16cm

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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.

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