Question

the length of a rectangleexcced it's breadth by 7cm. If the length decreased by 4cm and the breadth is increased by 3cm,the area of the new rectangle is the same as the area of the original rectangle. Find the length and the breadth of the original rectangle.

Answer 1

Let breadth be ( x ) cm and length be ( x + 7 ) cm

Area of rectangle = length breadth

Hence,

Area of this rectangle = x( x + 7 ) cm^2

When, length is decreased by 4cm i.e. ( x + 7 - 4 ) = ( x + 3 ) cm

Breadth is increased by 3 cm i.e. ( x + 3 ) cm

Area becomes = ( x + 3 )( x + 3 )

Given that area remains same,

$\rightarrow x( x + 7 ) = ( x + 3 )( x + 3 ) \\ \\ \rightarrow x^2 + 7x = x^2 + 9 + 6x \\ \\ \rightarrow 7x = 9 + 6x \\ \\ \rightarrow 7x - 6x = 9 \\ \\ \rightarrow x = 9$

According to the solution,

Breadth of original rectangle = x = 9 cm

Length of original rectangle = ( x + 7 ) = ( 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.